Title: Gravitational Physics with a Positive $\Lambda$: Fundamental Open Issues

In the positive cosmological constant sector, several basic questions in classical and quantum gravity, which were resolved some 40-50 years ago in the zero cosmological constant sector, still remain open. For example, a common requirement that scri of asymptotically de Sitter space-times be conformally flat turns out to be an unphysical and severe restriction that by fiat removes half of space-times we should consider. With or without this requirement, we still do not have a satisfactory notion of gravitational radiation or Bondi 4-momentum in exact GR, nor a positive energy theorem. Similarly, the standard constructions of `in' and `out' Hilbert spaces on scri that we routinely use (e.g. in the analysis of black hole evaporation) do not extend to space-times that are asymptotically de Sitter. In this talk I will present some illustrative examples of these quandaries and introduce a systematic approach to resolve the open issues.

Title: Turbulence and superradiance in black hole physics

Black holes are the elementary particles of gravity, and play a crucial role in fundamental physics, astrophysics, high energy physics and particle physics. In the last years, our ability to understand strongly nonlinear phenomena involving black holes has opened up a new Golden Age in the field. General Relativity's 99 years are being celebrated with many new developments, ranging from Cosmic Censorship tests in violent scenarios to constraints on particle physics with supermassive black holes. I will describe some of the current activity in the field, focusing on black hole superradiance and weak turbulence in confined systems.

Title: Fake hair for scalar tensor black holes

We will review modified gravity theories and in particular scalar tensor theories, the mildest of modifications, where we have an additional interacting scalar field coupling to the metric tensor. By means of a theorem given by Horndeski back in 1974 we will show the most general of these theories often called nowadays Galileon theory. We will examine a particular sub class of Horndeski theory which has interesting properties with respect to the cosmological constant problem. This carries the unfortunate name fab 4. We will then find black hole solutions of this subclass which in some cases will be identical to GR solutions. The novel ingredient will be the presence of a time and space dependent scalar. As we will see time dependence will birfucate no hair theorems and provide regular scalar tensor black holes with a non trivial scalar field.

Title: The analog of the Hawking effect in BECs

The Hawking effect from black holes is a milestone in modern Theoretical Physics, but its detection in the astrophysical context is unlikely. Thanks to Unruh, it is possible to look for the analog of the Hawking effect in condensed matter systems. We shall review the status of ongoing experiments and focus on the possibility to observe it in Bose-Einstein condensates through correlation measurements.

Title: Tensor calculus with free softwares: the SageManifolds package

After a brief review of computer algebra systems for tensor calculus, the new package SageManifolds will be presented. SageManifolds (http://sagemanifolds.obspm.fr) is an extension of the open source mathematics software Sage, implementing differential geometry and tensor calculus. As Sage, it is a free and based on the Python programming language. This last feature makes it easy to use for anybody with a basic knowledge of Python. Various applications of SageManifolds to general relativity will be demonstrated.

Title: Gamma-Ray Bursts (GRBs), decades of expansion

Gamma-Ray Bursts (GRBs) represent the most violent events of the Universe. Due to their beamed optical emission (called afterglow) they behave like intense lighthouses visible at cosmological distances. Multiwavelength observations of GRBs has led to deep implications on a broad set of subdisciplines, for instance, stellar evolution, gravitational waves, nucleosynthesis, collapses, cosmology, or the study of new populations of galaxies. I would review the most interesting observational aspects studied in the last years on long-duration GRBs, short-duration GRBs, high-redshift GRBs, Supernovae associated to GRBs and the host galaxies where these explosions tend to occur.

Title: Weakly regular spacetimes with T2 symmetry

I will present a theory of weak solutions to the Einstein equations under the assumption of T2 symmetry, when the initial data set (imposed in the initial value problem) satisfy certain weak regularity conditions only. I will establish the existence of global foliations whose time function coincide with the area of the orbits of the symmetry group, and then tackle the analysis of the global geometry of these weakly regular spacetimes. To this aim, in papers (written over the past ten years) in collaboration with J.M. Stewart, A.D. Rendall, or J. Smulevici, I have introduced several techniques to deal with weak solutions to the Einstein equations. Interestingly, these spacetimes may exhibit impulsive gravitational waves (a la Khan-Penrose) as well as shock waves. Papers are available at philippelefloch.org.

Title: Beyond Einstein's General Relativity

Modern astrophysical and cosmological models are faced with two severe theoretical diculties, that can be summarized as the dark energy and the dark matter problems. Relative to the former, it has been stated that cosmology has entered a 'golden age', in which high-precision observational data have conrmed with startling evidence that the Universe is undergoing a phase of accelerated expansion. Several candidates, responsible for this expansion, have been proposed in the literature, in particular, dark energy models and modied gravity, amongst others. One is liable to ask: What is the so-called 'dark energy' that is driving the acceleration of the universe? Is it a vacuum energy or a dynamical field ("quintessence")? Or is the acceleration due to infra-red modications of Einstein's theory of General Relativity? We analyze some of the modied theories of gravity that address these intriguing and exciting problems facing modern physics, and explore the foundations of gravitation theory, essential for constructions of modied theories of gravity.

Title: The Creation of Bosons, Fermions, Gravitational Perturbations and Waves in the Expanding Universe

Quantum field theory predicts that particles, perturbations and gravitational waves may be created from the vacuum in an expanding universe. The quantum field theory basis for this particle creation from vacuum was first shown and thoroughly studied in my Ph.D. Thesis (Harvard University, 1966) and my related papers (Phys. Rev. Lett,, 1968, and Phys. Rev. 1969 and 1971). I go over the physical basis for these processes that follow from quantum field theory and general relativity. The effect of the creation of perturbations and particles is observed today in the small temperature anisotropies of the isotropic CMB radiation. Furthermore, part of the recently observed B-wave polarization pattern of the CMB radiation may result from the creation of gravitational wave perturbations by the early expanding universe. Finally, I discuss the quantum field theory basis for the vacuum state of the exponentially expanding inflationary universe. I show how the inflationary vacuum state may arise by dynamical evolution from an initial Minkowski vacuum state in a flat space-time that spontaneously fluctuates to form some subregions undergoing inflationary exponential expansion.

Title: The universe could be dark, ma non troppo

We will present new insights into the dark phenomena, i.e., the recent acceleration of the universe linked to a sort of dark energy, and to the unknown dark matter. The study is based only on Eintein’s equations without cosmological constant, and on ordinary matter described as point masses. We will be limited, thereby, to the post -recombination epoch. We shall revise the outspread statement that a universe made of collission-less particles is well represented by dust, i.e; by an Einstein-de Sitter universe. Using well known results on the N-body problem expressed as a infinite series, and starting at zero order with the empty Milne universe, we shall get the formentioned EdS universe at the first order, but at the next one we shall obtain a cosmological model whose energy density could explain the dark phenomena. No exotic dark components are necessary in principle, but we need to know the redshift of formation of the dominant particles in the present epoch, that we identify with the galaxies. Thus, assuming that redshift to be of the order of 11, we shall get that the time evolution of the acceleration, and the supernovae luminous distance-redshift relation, are indistinguishable from the ones predicted by the ΛCDM model. However, if there was no realistic evolution model that could justify such an early galaxy formation epoch, then some quantity of dark energy would be necessary, ma non troppo.

Title: Gravitational double layers

Gravitational double layers, unlike their classical electromagnetic counterparts, are thought to be forbidden in gravity theories. I will prove, however, that they are feasible in, for instance, gravity theories with a Lagrangian quadratic in the curvature. This comes as a surprise, the potential consequences are tremendous, and new physical behaviours can be described. While a clear interpretation seems elusive, several doors are open. I will present the field equations for double layers, the new physical quantities arising, and several explicit examples. For further reading: http://cqgplus.com/2014/03/14/first-occurrence-of-a-double-layer-in-a-gravity-theory-found/, http://iopscience.iop.org/0264-9381/31/7/072002/article .

Title: Supermassive black hole astrophysics with pulsar timing arrays

Within this decade the detection of gravitational waves (GWs) may be a reality, opening a completely new window on the Universe. At nHz frequencies, pulsar timing arrays (PTAs) promise to detect the signal coming from the cosmological population of supermassive black hole binaries SMBHBs within the next few years. After rewiewing the astrophysics of SMBHBs, I will describe the current status of the PTA effort, and cast propspects of detection and astrophysical payouts.

Title: Binary neutron star merger: Gravitational waves and electromagnetic counter parts

The merger of binary neutron stars is one of most promising sources of gravitational waves. It is also a promising candidate for the central engine of short-hard gamma-ray bursts and a source of the strong transient electromagnetic signal that could be the counterpart of gravitational-wave signals. Numerical relativity is probably the unique tool for theoretically exploring the merger process, and now, it is powerful enough to provide us a wide variety of aspects of the binary-neutron-star merger. In this talk, I will summarize our current understanding of the entire merger event that is obtained by numerical-relativity simulations. In particular, I focus on the relation between the neutron-star equation of state and gravitational waves emitted during the late inspiral and merger phase, and observable electromagnetic signal that is likely to be emitted by the dynamical ejecta.

Title: Post-merger Oscillations in Binary Neutron Star Mergers

Because of the recent discovery of two-solar-mass neutron stars, the equation of state of high density matter is likely to be sufficiently stiff to allow for a long-lived remnant, when two neutron stars merge. The merger excites a number of oscillation modes, having large (nonlinear) amplitude, that are interesting as gravitational waves sources for second- and third-generation interferometric detectors. Apart from a dominant linear oscillation mode, additional nonlinear contributions appear. I discuss the main properties of these oscillations as well as the prospects of constraining the mass and radius (and thus the equation of state) with future detections.

Title: 2+1 black hole with SU(2) hair

It is well known that the 2+1-dimensional black hole is a portion of anti-de Sitter spacetime with identifications, and it is therefore described by a locally a flat AdS connection. It is less well known that this black hole is also a locally Lorentz-flat geometry. This means that any simply connected portion of this geometry can be consistently covered with a congruence of locally inertial frames, as is the case for Minkowski spacetime in Special Relativity. By exploiting the isomorphism between SO(1,2) and SU(2), the 2+1 black hole can be endowed with a locally flat but globally non-trivial SU(2) connection as well. For certain values of mass and SU(2) charge, this geometry admits globally defined Killing spinors, corresponding to perturbatively stable supersymmetric vacua. These black holes are exact solutions in a supersymmetric theory whose Lagrangian is related to graphene.

Title: Inflationary center manifold and slow-roll expansions

We develop center manifold and slow-roll expansions and approximants in a global state space setting for so-called attractor solutions for the minimally coupled scalar field with a quadratic potential in flat FLRW cosmology.

Title: Quantum correlations across cosmological horizons

We construct a simple minisuperspace model for the Schwarzschild-de Sitter space, in order to de develop a an exact quantization of the space-time. In this way, we determine the physiscal Hilbert space which allow us to study the possible quantum influence of regions of the universe that are not classically accesible.

Title: Gravitational waves from collapsars

The core of rapidly rotating, massive stars collapses by the end of their life cycle forming stellar mass black holes surrounded by accretion discs. This is the basic scenario defining a collapsar, nowadays the prototype of central engine for long gamma-ray bursts. We will show that under certain conditions, the collapse of the stellar core does not yield directly a black hole. Instead an intermediate, metastable phase forms: a proto-neutron star (PNS). The period during which the PNS can survive is long enough so that very peculiar gravitational wave signals can be produced. We will relate the features displayed by the gravitational waves with very definite events on the PNS and its surrounding matter. We will show that such events can be mapped to the evolution of the mass and the radius of the PNS throughout its (very short) lifetime.

Title: Symmetry operators and conserved currents

In this talk we will consider symmetry operators for the conformal scalar wave equation, the source-free Maxwell equation and the source-free massless Dirac equation on curved backgrounds. These are linear differential operators taking solutions to solutions. The symmetry operators are versatile tools and can for instance be used to construct higher order energy momentum tensors, that can be used to analyse decay of the fields. In this talk I will present conditions for existence of such operators. How the conditions for the symmetry operators for the different field equations are related will also be discussed. It turns out that existence of symmetry operators are linked to the existence of conserved currents. This link will also be explored.

Title: Loop quantum cosmology: lessons from the polymerized harmonic oscillator.

We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies that the point spectrum consists of bands similar to the ones appearing in the treatment of periodic potentials. With the help of this result we give a construction of a separable Hilbert space that can be used in the context of other polymer quantum mechanical systems including those of loop quantum cosmology.

Title: Do transient white holes have a place in nature?

The white-hole sector of Kruskal solution is almost never used in physical applications. However, it might have the solution of many of the problems associated with gravitational collapse and evaporation. In this talk we will try to draw attention over some bouncing geometries that make a democratic usage of the black and white sectors. We will argue that these type of behaviour could be perfectly natural in some approaches to the next physical level beyond classical general relativity.

Title: Vacuum Spacetimes with a Constant Weyl scalar

Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant) with a constant non-zero Weyl eigenvalue are considered. For type Petrov II and D this assumption alone is sufficient to allow one to prove that the non-repeated eigenvalue necessarily has the value 2?/3 and it turns out that the only possible spacetimes are some Kundt-waves considered by Lewandowski which are type II and a Robinson-Bertotti solution of type D. For Petrov type I the only solution in which all three Weyl eigenvalues are constant turns out to be a homogeneous pure vacuum solution found long ago by Petrov using group theoretic methods. These results can be summarised by the statement that the only vacuum spacetimes with constant Weyl eigenvalues are either homogeneous or are Kundt spacetimes. This result is similar to that of Coley et al.who proved their result for general spacetimes under the assumption that all scalar invariants constructed from the curvature tensor and all its derivatives were constant. Some preliminary results are also presented for Petrov Type I vacua in which either only one of the Weyl eigenvalues is constant or in which the ratios of the Weyl eigenvalues are constants. In particular in each case there is a simple algebraic relation between the Newman-Penrose Weyl tensor components and the `cross-ratio' of the optical scalars ??-?? of the associated principal null tetrad of the Weyl tensor.

Title: Computation of Fermi and observational coordinates

Fermi and observational coordinates are strongly related to the concept of simultaneity of a given observer. Fermi coordinates describe simultaneity from a spacelike point of view, i.e. the events that are simultaneous in the local inertial proper system of the observer. On the other hand, observational coordinates describe simultaneity from a lightlike point of view, i.e. the events that are observed simultaneously by the observer, and they are particularly important in the study of gravitational lensing. Moreover, both of them are used for defining some intrinsic concepts of relative velocity. There are some methods for computing these coordinates in a general spacetime, but they involve Taylor expansions that become very complex for achieving high accuracy. In this work, we present an alternative numerical method that can be applied to any observer in any spacetime. This method is based on an iterative algorithm and so, for increasing accuracy, we just have to make more iterations without additional difficulty. Nevertheless, there are some open problems about convergence in general.

Title: Killing vector analysis in the GHP formalism

A method for constructing the Killing vectors of a spacetime with an intrinsically defined GHP tetrad was developed by Edgar and Ludwig in Gen. Rel. Grav. 32, 637 (2000).They defined a generalised Lie derivative operator that reduces to the usual Lie derivative when acting on zero-weighted quantities. To obtain the Killing equations one then act with the commutators of this derivative and the GHP operators on zero-weighted scalars (the intrinsic coordinates). In this work we extend the method to a class of spacetimes with a null rotation isotropy, so that an intrinsic GHP tetrad cannot be completly found. The Killing vectors for some cases, including conformally flat pure radiation metrics, are then determined and the results are compared with other methods.

Title: Statistical moments for classical and quantum cosmology

We compare the classical and quantum description of systems with a finite number of degrees of freedom with an effective formalism based on statistical moments. Within this formalism the similarities and differences between the classical and quantum evolution of an initial probability distribution are made apparent. Inequalities obeyed by these statistical moments, and in particular uncertainty relations that bound the information that it is possible to obtain from a quantum system, are derived at high orders. We study applications to simple mechanical systems like the free particle and the harmonic oscillator. In addition we analyze the pure quartic oscillator as an example of anharmonic system. Finally we revisit the application to a simple cosmological systems of this formalism: the homogeneous and isotropic universe with a massless scalar field as matter content and with positive cosmological constant.

Title: Absence of cosmological constant problem in special relativistic field theory of gravity

The principles of quantum field theory in flat spacetime suggest that gravity is mediated by a massless particle with helicity $\pm 2$, the so-called graviton. It is regarded as textbook knowledge that, when the self-coupling of a particle with these properties is considered, the long wavelength structure of such a nonlinear theory is fixed to be that of general relativity. However, here we show that these arguments conceal an implicit assumption which is surreptitiously motivated by the very knowledge of general relativity. This is shown by providing a counterexample: we revisit a nonlinear theory of gravity which is not structurally equivalent to general relativity and that, in the non-interacting limit, describes a free helicity $\pm 2$ graviton. We explicitly prove that this theory can be understood as the result of self-coupling in complete parallelism to the well-known case of general relativity. The assumption which was seen as natural in previous analyses but biased the result is pointed out. This special relativistic field theory of gravity predicts the decoupling of vacuum zero-point energies of matter and passes all the known experimental tests in gravitation.

Title: Excision technique in constrained formulations of Einstein equations: collapse scenario.

In this talk I will present a new excision technique used in constrained formulations of Einstein equations to deal with black holes in numerical simulations. I will show the applicability of this scheme in several scenarios. In particular, I will present the dynamical evolution of the collapse of a neutron star to a black hole using the CoCoNuT code in which this excision technique has been implemented.

Title: Inertial forces in General Relativity

Inertial forces are fictitious forces that arise and play a dominant role in the 1+3 description of the motion of a test particle with respect to a family of observers. The most basic example is the Newtonian field (for weak fields), other the so-called "gravitomagnetic" field. In this talk this problem is revisited; an exact equation describing the inertial forces for arbitrary frames on arbitrary spacetimes is derived, by means of suitable connection defined on the bundle of vectors orthogonal to a congruence of time-like curves. It manifests that the gravitomagnetic field, at a fundamental level, consists of a combination of two effects of independent origin: the vorticity of the observer congruence, plus the angular velocity of rotation, relative to Fermi-Walker transport, of the triad of spatial axes that each observer ?carries? with it. Such formulation encompasses the different gravitomagnetic fields studied in the literature; notable cases include the fields arising in two well known reference frames defined in stationary axisymmetric spacetimes: the one associated to the Killing observers, and the so-called "locally non-rotating frames", associated to the zero angular momentum observers. Newtonian analogues of the different gravitomagnetic fields and exact analogies with electromagnetism are put forth. The experimental detection of the effects described by these fields is also briefly discussed.

Title: Testing vector-tensor gravity with current cosmological observations

A certain vector-tensor theory of gravitation (hereafter VT) has been recently applied to cosmology (Phys. Rev. D, 89, 2014, 044035). It leads to encouraging results. The zero order energy density of the vector field accounts for the cosmological constant. It has been recently proved that the VT vector field cannot play the role of the electromagnetic field. The evolution of the VT scalar perturbations is different in VT and general relativity. Tensor fluctuations evolve in the same way in both theories. Here, the VT evolution equations of the scalar modes are appropriately written, and the initial conditions at high redshift ?necessary for numerical integration-- are summarized. The codes COSMOMC and CAMB are modified for applications to VT cosmology and, then, by using the new version of COSMOMC, statistical methods (Markov chains) allow us to fit theoretical VT predictions with current data about cosmic microwave background anisotropies and about other complementary observations. New results are compared with previous ones which strongly supported VT cosmology. Previous results were based on WMAP7 data, supernovae Ia observations, and a minimal model involving seven cosmological parameters.

Title: Spacetime analysis of primordial perturbations during slow roll inflation.

We perform a complementary study to the primordial power spectrum predicted by slow roll inflation using a spacetime viewpoint. We consider two-point correlators of primordial perturbations in a quasi de Sitter background. For largely separated points this procedure nicely recovers the expected nearly scale invariance, which is compatible with observations. We also discuss some additional implications.

Title: Probing f(R) gravity with PLANCK data on cluster pressure profiles

Models of f(R) gravity that introduce corrections to the Newtonian potential in the weak field limit are tested at the scale of galaxy clusters. These models can explain the dynamics of spiral and elliptical galaxies without resorting to dark matter. We compute the pressure profiles of 579 galaxy clusters assuming that the gas is in hydrostatic equilibrium within the potential well of the modified gravitational field. The predicted profiles are compared with the average profile obtained by stacking the data of our cluster sample in the Planck foreground clean map SMICA. We find that the resulting profiles of these systems fit the data without requiring a dominant dark matter component, with model parameters similar to those required to explain the dynamics of galaxies. Our results do not rule out that clusters are dynamically dominated by Dark Matter but support the idea that Extended Theories of Gravity could provide an explanation to the dynamics of self-gravitating systems and to the present period of accelerated expansion, alternative to the concordance cosmological model.

Title: Numerical Brill-Lindquist Initial Data with a Schwarzschildean End at Spatial Infinity

We construct numerically time-symmetric initial data that are Schwarzschildean at spatial infinity and Brill-Lindquist in the interior (specifically a two black hole system is considered). The transition between these two data sets takes place along a finite gluing annulus equipped with an axisymmetric Brill wave metric. We show that the latter can be chosen in such a way that the smooth transition from the two black hole data in the interior to the Schwarzschildean end at spatial infinity is guaranteed. In addition, we investigate the dependence of the ADM mass of our construction on the details of the gluing procedure. The construction is based on an application of Corvino's gluing method using Brill waves due to Giulini and Holzegel.

Title: On evaporation of Randall-Sundrum black holes.

We investigate possibilities of experimental search for new physics which is predicted by Randall-Sundrum II gravity model. Also we obtained the law of evaporation for Dadhich-Rezania black hole solution and Abdolrahimi-Page black hole solution within RS II. Thus we look for cosmological tests of these theory via a study of gamma-ray bursts from primordial black holes radiation.

Title: The Gravity Apple Tree

The quest of man for the fundamental principles of nature?s laws is at an exciting moment. Obscure new phenomena, commonly explained as dark matter, dark energy and inflation has pushed into a crisis the standar paradigm of physics, general relativity and cosmology. At times when profesions are ultraspecialized is quite a job for legos to have a sintetic view of the roads explored and their fruits. The Apple Gravity Tree is a genealogical tree of gravitation theories intended to ilustrate the bulk of knowledge in this matter. It?s a mental map of the generic branches of the gravitation theories developed during the 20th century until 2013. Ten main branches emerge from the main trunk, which represents, in its middle core, the theory of general relativity (GR) of Albert Einstein. The branches emerge when different principles (matemathic, physical, philosophical or metaphysical) are followed in order to investigate some specific problem.

Title: Improving on numerical simulations of nonlinear CMB anisotropies

The Adaptative-Particle-Particle-Particle-Mesh (AP3M) Hydra Code plus an appropriate ray-tracing procedure was used, in Fullana et al. ApJ 712, 367 (2010), to perform an exhaustive analysis of the weak lensing anisotropy. Other nonlinear CMB anisotropies as the Rees-Sciama and the Sunyaev-Zel?dovich effects may be are also being studied by using the same tools (Hydra codes plus ray-tracing). We present here our advances in the study of the nonlinear CMB anisotropies. Such advances are based on the use of better simulations with greater particle densities and appropriate softening. Other parameters are also adjusted to get good enough estimates. Thus, we improve on a previous paper (Puchades et al. MNRAS 370, 1849 (2006)) where the Rees-Sciama effect was studied with PM simulations, we estimate three point correlations in the maps of the lensing effect, and so on.

Title: McGehee regularization of general SO(3)-invariant potentials and applications to stationary and spherically symmetric spacetimes

The McGehee regularization is a method to study the singularity at the origin of the dynamical system describing a point particle in a plane moving under the action of a power-law potential. It was used by Belbruno and Pretorius to perform a dynamical system regularization of the singularity at the center of the motion of massless test particles in the Schwarzschild spacetime. In this paper, we generalize the McGehee transformation so that we can regularize the singularity at the origin of the dynamical system describing the motion of causal geodesics (timelike or null) in any stationary and spherically symmetric spacetime of Kerr-Schild form. We first show that the geodesics for both massive and massless particles can be described globally in the Kerr-Schild spacetime as the motion of a Newtonian point particle in a suitable radial potential and study the conditions under which the central singularity can be regularized using an extension of the McGehee method. As an example, we apply these results to causal geodesics in the Schwarzschild and Reissner-Nordstr\"om spacetimes. Interestingly, the geodesic trajectories in the whole maximal extension of both spacetimes can be described by a single two-dimensional phase space with non-trivial topology. This topology arises from the presence of excluded regions in the phase space determined by the condition that the tangent vector of the geodesic be causal and future directed.

Title: On the conservation of Superenergy and its applications

In this work we present a geometric identity involving the Bel-Robinson tensor which is formally similar to the Sparling identity (which involves the Einstein tensor through the Einstein 3-form). In our identity the Bel-Robinson tensor enters through the {\em Bel-Robinson 3-form} which, we believe, is introduced in the literature for the first time. The meaning of this identity is that it is possible to formulate a {\em generic} conservation law for the quantity represented by the Bel-Robinson tensor (superenergy). We also show how one can use the Bel-Robinson 3-form to estimate the components of the Bel-Robinson tensor which are computed with respect to the causal elements of a frame. This estimate could be useful in a global existence proof of the solutions of a theory of gravitation in dimension four.

Title: Viability the matter bounce scenario

The CMB map provided by the {\it Planck} project constrains the value of the ratio of tensor-to-scalar perturbations, namely $r$, to be smaller than $0.11$ (95 \% CL). This bound rules out the simplest models of inflation. However, recent data from BICEP2 is in strong tension with this constrain, as it finds a value $r=0.20^{+0.07}_{-0.05}$ with $r=0$ disfavored at $7.0 \sigma$, which allows these simplest inflationary models to survive. The remarkable fact is that, even though the BICEP2 experiment was conceived to search for evidence of inflation, its experimental data matches correctly theoretical results coming from the matter bounce scenario (the alternative model to the inflationary paradigm). More precisely, most bouncing cosmologies do not pass {\it Planck's} constrains due to the smallness of the value of the tensor/scalar ratio $r\leq 0.11$, but with new BICEP2 data some of them fit well with experimental data. This is the case with the matter bounce scenario in $F(T)$ gravity.

Title: An upper bound on the number of Killing-Yano tensors

We present a formula which provides an upper bound on the number of Killing-Yano tensors, as well as closed conformal Killing-Yano tensors, for a given metric. The formula is applied to some physical metrics and it is shown that, for example, the Kerr metric admits only two Killing vector fields, one rank-2 and no rank-3 Killing-Yano tensors.

Title: A perspective on black hole horizons from the quantum charged particle

We point out a structural similarity between the characterization of black hole apparent horizons as stable marginally outer trapped surfaces (MOTS) and the quantum description of a non-relativistic charged particle moving in given magnetic and electric fields on a closed surface. Specifically, the MOTS-spectral problem corresponds to a stationary quantum particle with a formal fine-structure constant $\alpha$ of negative sign. Such analogy may provide clues to the study of the spectrum of the (non-selfadjoint) MOTS-stability operator in comparison with the (selfadjoint) Hamiltonian of the quantum charged particle. Moreover, this perspective might open an avenue to the spinorial treatment of apparent horizon (MOTS-)stability and to the introduction of semiclassical tools to explore some of the qualitative aspects of the black hole spectral problem.

Title: Gravitational waves from hypermassive neutron stars.

We will show results from simulations of irrotational and spinning binary neutron star mergers with nuclear physics equations of state. The models which form a hypermassive neutron star exhibit a feature rich gravitational wave spectrum, which we relate to the dynamics of the source. For this we study the evolution and interplay of highly nonlinear oscillations excited by the merger. Further, we investigate the influence of the neutron star (aligned) spin on the properties of the merger remnant, and estimate the amount of ejected matter.

Title: Magnetized binary neutron star merger simulations on K

We performed numerical relativity-magneto hydrodynamical simulations of binary neutron star merger on the Japanese supercomputer K. The grid resolution of 70 m is highest among the binary neutron star merger simulations done so far and we did an in-depth resolution study to figure out the amplification mechanism of magnetic fields during the binary neutron star merger. We found the Kelvin-Helmholts instability developed in the shear layer at the merger significantly amplifies the magnetic field. A hyper-massive neutron star formed after the merger is subject to the non-axisymmetric magneto-rotational instability. These two amplification mechanisms do not work with an insufficient resolution. The star collapses to a black hole and a formed accretion disk is strongly magnetized a priori. We found a coherent toroidal magnetic field inside the disk and not a coherent poloidal field above the black hole even after 60 ms after the black hole formation.

Title: Minimal length and small scale structure of spacetime

Many generic arguments suggest the existence of a minimal spacetime length $L_0$. I show that such a length scale can be introduced in a Lorentz covariant manner by a non-local, disformal coupling of the metric to the Synge world function bi-scalar. I further demonstrate that the same non-analytic structure of the deformation which renders a perturbative expansion in $L_0$ meaningless, can also leave $O(1)$ effects in the limit $L_0 -> 0$. In particular, the $O(1), L_0$ independent, modification to the Einstein-Hilbert lagrangian turns out to be proportional to $R_{ab} t^a t^b$, suggesting the transmutation $R -> R_{ab} t^a t^b$ of the classical gravitational lagrangian, with the arbitrary normalized vectors $t^a$ at each spacetime event representing the vestige of the small scale structure of spacetime. I discuss several implications of this result, and in particular it's connection with the idea that the cosmological constant itself might be related to some non-local vestige of the small scale structure of spacetime

Title: Adiabatic regularization for scalar and spin-1/2 fields

The extension of the adiabatic regularization method to spin-1/2 fields requires a self-consistent adiabatic expansion of the field modes. We provide here the details of such expansion, which differs from the WKB ansatz that works well for scalars, to firmly establish the generalization of the adiabatic renormalization scheme to spin-1/2 fields. We also provide a general overview of the adiabatic method to perform renormalization of relevant expectation values. We focus on the analytic computation of the renormalized stress-energy tensor for Dirac fermions in de Sitter spacetime.

Title: On cosmic quantum tunneling from "nothing"

The Einstein field equations for any spherically symmetric metric and a geodesic perfect fluid source are cast in a canonical simple form, both for Lorentzian metrics and for instantons. The general solution for both kinds of metrics is explicitly written in the particular case of the Lema{\^{\i}}tre-Tolman-Bondi family, and more specifically in the case of a general $\Lambda$-Friedmann-Lema{\^{\i}}tre-Robertson-Walker universe. Using these specific solutions (including of course the instanton version) we study wether the probability of quantum creation of our Universe from ``nothing'' vanishes or not. It is found, in accordance with previous results, that only the closed model can have a non zero probability of been quantically created. To obtain this result we lay on general assumptions which are satisfied in the particular creation case considered some time ago by Vilenkin. Assuming a suggestion by Fomin and Tryon (that the energy of a universe, coming from a vacuum fluctuation, vanishes), these probabilities would be in a minimal accordance with what is suggested by the value (zero or infinite) of the intrinsic energy for the different (closed, flat or open) $\Lambda$-Friedmann-Lema{\^{\i}}tre-Robertson-Walker models.

Title: Cauchy horizon stability and mass inflation with a cosmological constant.

The existence and stability of Cauchy horizons is intimately related to the question of global uniqueness for the Einstein equations and, in particular, to the celebrated strong cosmic censorship conjecture. To study this, we consider the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the outgoing part of the null initial hypersurface prescribed by a (complete) subextremal Reissner Nordström black hole event horizon, with non-vanishing charge, and the remaining data otherwise free, verify if the corresponding Maximal Globally Hyperbolic Development is future inextendible as a suitably regular Lorentzian manifold. This is a direct extension of the framework of [1] with the introduction of a cosmological constant in the field equations. We generalize the results of Dafermos concerning the stability of the radius function, for a cosmological constant of any sign. This has the remarkable consequence of allowing continuous extensions of the metric across the Cauchy horizon. We also analyze the mass inflation scenarios and identify large choices of parameters for which the Hawking mass remains bounded. Then we carefully unveil the consequences of this last fact concerning the existence of regular extensions of the metric beyond the Cauchy horizon. [1] Dafermos, M., Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations. Ann. of Math. (2) 158 (2003), no. 3, 875928. Joint work with: Pedro Girão (IST--ULisboa/CAMGSD), José Natário (IST--ULisboa/CAMGSD) and Jorge Drumond Silva (IST--ULisboa/CAMGSD)

Title: Cosmological constrains on fast transition Unified Dark Matter models

In this work we show the results from applying a Unified Dark Matter (UDM) model with fast phase transitions to a set of cosmological data. Two different functions are tested for this transition, and the feasibility of both models is explored using CMB shift data from Planck, Galaxy Clustering data and Union2.1 SNe Ia. These new models are also statistically compared with the LCDM and quiessence models using Bayes factor after calculating their statistical evidence. Bayesian inference does not discard the UDM models in favor of LCDM.

Title: Can topological defects mimic the BICEP2 B-mode signal?

In this talk I will summarize the signatures of topological defects on the CMB anisotropies and I will compare these predictions with the latest measured CMB polarization data: BICEP2. I will give updated constraints on topological defects derived from different models considering the most modern CMB data.

Title: Extended models of gravity in SNIa cosmological data using genetic algorithms.

In this talk I will briefly explain the advantages of using genetic algorithms on any measured data but specially astronomical ones. This kind of algorithms are not only a better computational paradigm, but they also allow for a more profound data treatment enhancing theoretical developments. As an example, I will use the SNIa cosmological data to fit the extended metric theories of gravity of Carranza et al. (2013, 2014) -see D.A. Carranza's talk also- showing that the best parameters combination deviate from theoretical predicted ones by a minimal amount. This means that these kind of gravitational extensions are statistically robust and show that no dark matter and/or energy is required to explain the observations.

Title: Evolution of Semilocal String Networks

In this talk I will summarise our work about the analysis of semilocal string networks which is divided in three different parts. In the first part we analyse the large-scale properties of the simulation based on the largest and most accurate field theory simulations of semilocal strings to date. In the second part we study in detail the evolution of semilocal segment population and provide a quantitative comparison between our numerical simulations and analytic models. Finally in the third part of this work we study the velocities of semilocal string segments in order to improve our comparison between numerical simulations and analytic models. Taking into account that this is still work in progress we will concentrate on the methodology and give some preliminary results.

Title: Relativistic low angular momentum accretion

I will report on the first phase of the joint numerical project with J.A. Font and M. Pirog. We investigate low angular momentum accretion of inviscid fluids on black holes. The aim of this work is to promote previous Newtonian models to fully relativistic setting. The staring point of those simulations is the Bondi-type accretion solution, perturbed by adding a small amount of angular momentum. Results of both two and three dimensional simulations will be discussed, emphasizing the similarities and differences with Newtonian models.

Title: Extended Kerr-Schild spacetimes of any dimension

We study geometric and algebraic properties of extended Kerr-Schild spacetimes (xKS), i.e. an extension of the Kerr-Schild (KS) ansatz where, in addition to the null KS vector, a spacelike vector field appears in the metric. In contrast to the KS case, it turns out that xKS spacetimes with a geodetic KS vector are not necessarily algebraically special and we obtain, in general, only a necessary condition under which the KS vector is geodetic. However, it is shown that this condition becomes sufficient if we appropriately restrict the geometry of the null and spacelike vector fields. Examples of xKS spacetimes belonging to the Kundt class and also expanding xKS spacetimes, namely the CCLP black hole, are provided and briefly discussed.

Title: Topology of the Misner Space and its $g$-boundary

Many apparent space-time pathological behaviours can be imputed to the lack of a truly understanding of the geometry. On the other hand, intrinsic pathologies are the trademark of singular space-times. Both situations are present in the Misner space. In our talk we will provide topological arguments that explain neatly where both king od pathologies come from by obtaining an explicit base of the topology of the complete Misner space ${R}^{1,1}/boost$. Besides, we prove that some parts of this whole space, that behave like topological boundaries, are equivalent to the g-boundary of the Misner space.

Title: Semiclassical energy conditions and wormholes.

The nonlinear energy conditions, which behave much better than the classical linear energy conditions in the presence of semiclassical quantum effects, will be presented. Furthermore, quantum extensions of these nonlinear energy conditions will be considered. Although analogous quantum extensions for the linear energy conditions are not always satisfied as one enters the quantum realm, they can be used for constraining the violation of the classical conditions. Thus, the existence of wormholes supported by a fluid which violates the null energy condition in a controlled way is of particular interest.

Title: Propagation of an optical vortex beam around a Kerr black hole

Recently, an optical vortex beam, which have helical phase front, are actively investigated in the optical physics. Using the eikonal approximation, we will show that orbits of an optical vortex beam deviate from null geodesics around a Kerr black hole. This is caused by the interaction between an optical vortex and the angular momentum of the Kerr black hole.

Title: Astrophysical constraints and insights on extended relativistic gravity

In this talk I will give precise details to support that observations of gravitational lensing at scales of individual, groups and clusters of galaxies can be understood in terms of non-Newtonian gravitational interactions with a relativistic structure compatible with the Einstein Equivalence Principle. This result is derived on very general grounds without knowing the underlying structure of the gravitational field equations. As such, any developed gravitational theory built to deal with these astrophysical scales needs to reproduce those results.

Title: General relativistic simulations of thick self-gravitating accretion disks around tilted Kerr black holes.

We simulate the dynamics of self-gravitating tori around tilted Kerr black holes in full 3D general relativity. We investigate the effects of the tilt angle between the disk angular momentum and black hole spin vectors on the dynamics of these systems, being particularly interested in a possible imprint of the tilt angle in the gravitational wave signal as the torus evolves in the tilted spacetime. We also investigate the behaviour of the BH in the tilted evolution, checking for its precession due to the evolution of the disk. Furthermore we want to quantify the effects the tilted configuration has on quasi-periodic oscillations (QPO) in the disk. We simulate the systems using the Einstein Toolkit, using the thorn McLachlan for the evolution of the spacetime via the BSSN formalism and the thorn GRHydro for the evolution of the hydrodynamics, using a 3D Cartesian mesh with adaptive mesh refinement (AMR).

Title: Extended theories of gravity with generalized energy conditions.

The consideration of the further degrees of freedom related to scalar fields and curvature invariants of of Extended Theories of Gravity lead us to derive generalized energy conditions. It is shown that the standard weak, dominant, null and strong energy conditions can be recovered once further terms in Extended Gravity are grouped in a tensor $H^{ab}$ and a coupling $g(\Psi^i)$. The latter can be interpreted in effective Einstein field equations, as corrections to the energy-momentum tensor of matter. The energy conditions rely on the satisfaction of inequalities related to the combined quantity $T^{ab}/g-H^{ab}$. The formal validity of such inequalities does not assure some basic requirements such as the attractive nature of gravity, so that the energy conditions have to be considered in a wider sense. Particular examples of extended theories such as scalar-tensor gravity, $f(R)$ gravity and $f(\cal G)$ gravity are given.

Title: Connecting entropy and gravitational energy in spacetime thermodynamics

We make an attempt to connect entropy and gravitational energy in Jacobson's spacetime thermodynamics.

Title: Electric Quench in AdS/CFT

An electric quench, a suddenly applied electric field, would cause a thermalization of confining systems as well as a deconfinement transition. We use the AdS/CFT correspondence for N=2 supersymmetric QCD which has a confining meson sector, to analyze the transitions. We find that the electric quench causes the deconfinement transition even when the magnitude of the applied electric field is weaker than the critical value for the static case. The time dependence is crucial for this phenomena, and the gravity dual explains it as an oscillation of a D-brane in the bulk AdS spacetime. Interestingly, the deconfinement time takes only discrete values as a function of the magnitude of the electric field. Together with a turbulent behavior which we compute as a time-dependent energy flow to higher resonance modes of vector/scalar mesons, we show that the deconfinement is a consequence of a coherent condensation of highly excited mesons.

Title: Cracking of anisotropic spheres in General Relativity revisited.

We consider the cracking formalism for self-gravitating matter configurations, introduced by L. Herrera several years ago. We have found that, anisotropic matter configurations (i.e. unequal radial and tangential stresses: (P?P?), described by two barotropic equation of state of the form P=P(?) and P? (?), will be cracking-stable if $2( v^2-(v?)^2 )/r +(v^2)' ?0$, where v and v? are the radial and tangential sound speeds, respectively. This is valid for dependent density perturbations affecting the pressure gradient within the configuration. We show with several examples, that this criterion can be useful to study instabilities for isotropic and anisotropic matter distributions.

Title: Particle and photon orbits in McVittie spacetime

McVittie spacetimes represent an embedding of the Schwarzschild field in isotropic cosmological backgrounds. Depending on the scale factor of the background, the resulting spacetime may contain black and white hole horizons, as well as other interesting boundary features. In order to further clarify the nature of these spacetimes, we address this question: do there exist bound particle and photon orbits in McVittie spacetimes? Considering first circular photon orbits, we obtain an explicit characterization of all McVittie spacetimes for which such orbits exist. We show that McVittie spacetimes with background scale factor corresponding to a $\Lambda$-CDM cosmology do not admit circular photon orbits. However, we prove that in two large classes of McVittie spacetimes, there are bound particle and photon orbits: future-complete non-radial timelike and null geodesics along which the areal radius $r$ has a finite upper bound. These geodesics are asymptotic at large times to circular orbits of a corresponding Schwarzschild or Schwarzschild-de Sitter spacetime. The existence of these geodesics lays the foundations for and shows the theoretical possibility of the formation of accretion disks in McVittie spacetimes. We also summarize and extend some previous results on the global structure of McVittie spacetimes. The results on bound orbits are established using centre manifold and invariant manifold techniques from the theory of dynamical systems.

Title: Quasilocal Angular Momentum in (2+2) formalism

A new definition of quasilocal angular momentum of gravitational field will be given from one of the constraints of (2+2)-canonical formalism of Einstein's theory. The new definition has several attractive properties. It provides a usual commutation relation of angular momentum at null infinity. And it also gives exact values for Minkowski and Kerr spacetime at null infinity. The relation between our definition and Rizzi's one will be also discussed.

Title: Asymptotic properties of gravitational and electromagnetic fields in higher dimensions

We investigate decay properties of the Weyl tensor as one approaches infinity along a congruence of null geodesics in n-dimensional Einstein spacetimes. The possible ?r-dependence? of the various Weyl components is analyzed in the $n>$4 Newman-Penrose formalism. Depending on the choice of boundary conditions, various fall-off behaviors are possible, in which the leading term can be, e.g., of type II or N. In particular, conditions necessary for asymptotic flatness lead to either a Schwarzschild-like fall-off, or a radiative ?1-n/2? fall-off (in agreement with previous results by Hollands and Wald and by Godazgar and Reall). Qualitative differences that arise in the presence of a cosmological constant are discussed, as well as significant differences with the well-known four dimensional results. A similar analysis is also applied to test Maxwell fields in the same background spacetimes, and it is again found that the peeling behavior is different when $n>4$ - also depending on a choice of ?electric? or ?magnetic? boundary conditions. Properties of general Maxwell p-forms will also be mentioned. [Marcello Ortaggio, Alena Pravdová, arXiv:1403.7559]

Title: General relativistic Boltzmann equation, formulated for neutrino transport in supernovae, solved by numerical spectral methods

I will show how to adapt the general relativistic Boltzmann equation to the neutrino transport problem. A formulation that is convenient to be solved numerically with spectral methods will be shown, along with some numerical test cases from a new code developed to study the neutrino transport in supernovae.

Title: Axially Symmetric Relativistic Thin Disks Immersed in Spheroidal Matter Haloes

Two infinite families of axially symmetric relativistic thin disks of dust immersed in spheroidal matter haloes are presented. The disks are obtained from solutions of the Einstein equations for an axially symmetric conformastatic spacetime in which the metric tensor is characterized only by one metric function. By introducing a finite discontinuity on the first derivatives of the metric tensor, solutions with a singularity of the delta function type are obtained, so describing thin disks. The nonzero components of the energy-momentum tensor, both for the disk and the halo, are obtained from the Einstein equations. In this way, the energy densities and pressures of the sources are determined. By imposing the fulfillment of all the energy conditions we obtain a constraint over the solutions, in such a way that the metric function can be properly expressed in terms of a solution of the Laplace equation. By using the solution to Laplace equation in cylindrical coordinates we find infinite disks and by using the solution to Laplace equation in oblate spheroidal coordinates we find finite disks. In both cases we obtain particular solutions with energy densities and pressures well behaved everywhere. We also show that the masses of de disks and the haloes are finite even when densities are infinite. Finally we solve the geodesic equation for circular orbits in the plane of the disk to get the rotational curves.

Title: Keplerian rotation curves vs. central mass in accretion disks in the first post newtonian approximation.

Purely newtonian results have shown that the self-gravitation of the disk in Keplerian accreting disk systems with polytropic gas speeds up its rotation. The rotational frequency is larger than that given by the well known strictly Keplerian formula which takes into account the central mass only. Thanks to this analysis we obtained important informations about relation between central mass and mass of the disk in such systems. Furthermore, we have shown that this method can be used to estimate mass of the disk in some class of astronomical objects. In our recent work we show how the analogous effect looks like in the first post-newtonian approximation. Delivering a numerical data I would like to present our results and discuss similar problem which I presented in Benasque last year but this time in 1PN regime.

Title: Type N universal spacetimes

We study a special class of spacetimes, so called universal spacetimes that solve vacuum field equations of {\em all} gravitational theories with the Lagrangian constructed from the metric, the Riemann tensor and its derivatives of arbitrary order. Trivial examples of such spacetimes are Minkowski and (A)dS. It is also known for some time that certain pp-waves are universal, however, the class of universal spacetimes is much broader. We show that universal spacetimes are necessarily CSI (spacetimes with all polynomial curvature invariants being constant). Then, we focus on type N and III universal spacetimes in arbitrary dimension and prove that a type N spacetime is universal if and only if it is Einstein type N Kundt. We also show that a subclass of Einstein type III Kundt spacetimes admitting a recurrent null vector is universal. This talk is based on arXiv:1311.0234 in collaboration with S. Hervik and A. Pravdova.

Title: Type III and II universal spacetimes

We will discuss our recent results on type II universal spacetimes in arbitrary dimension.

Title: Relativistic positioning in Schwarzschild space-time

In the Schwarzschild space-time created by an idealized static spherically symmetric Earth, two approaches --based on relativistic positioning-- may be used to estimate the user position from the proper times forecast by four satellites. In the first approach --the most coherent one-- satellites and photons move in the Schwarzschild space-time. This approach is a first order one in the dimensionless parameter GM/r (with the speed of light c=1). In the second approach, satellites move in the Schwarzschild space-time --as in the first one-- but the photons emitted by the satellites follow null geodesics of the Minkowski space-time assymptotic to the Schwarzschild geometry. This assumption leads to positioning errors since the photon world lines are not geodesics of any Minkowski geometry. Hence, the two approaches give different inertial coordinates for a given user. These differences are estimated and appropriately represented for users located inside a great region surrounding Earth. The resulting values (errors) are small enough to justify the use of the second approach, which is the simplest and the most manageable one. The satellite evolution mimic that of the GALILEO global navigation satellite system.

Title: Post-Newtonian limits for Randall-Sundrum model

Parametrized post-Newtonian formalism is one of the standard methods of experimental check of gravity theories and limiting the model parameters. In this work we consider the PPN-paramertization of Randall-Sundrum II black hole solutions and show that these solutions are in good agreement with the GR predictions and the observation results.

Title: Revisiting Hartle's model: on the continuity of the metric functions

We explore the perturbative stationary and axisymmetric matching around a spherically symmetric background static matched configuration to second order between a rotating perfect fluid interior and an asymptotically flat vacuum exterior. To do that we provide a consistent analysis using modern perturbative theory, and, in particular, the theory of perturbative matchings to second order by Mars (2005). The particularisation to Hartle's setting, i.e. the explicit assumptions used in the original work by Hartle (1967), thus provides a firm ground where to study the importance (or lack thereof) of the implicit assumptions made to construct the original model and further developments.

Title: Application of Numerical Relativity to cosmological spherical collapse

This work aims to apply tools of Numerical Relativity to the problem of spherical collapse on a dynamical cosmological background. The study of this last phenomenon is usually done either by assuming the Newtonian limit for the local gravitational fields which are then computed on an isolated Friedmann background or by considering the inner part of the density fluctuation to assume its own cosmological solution that gets separate to the background as time evolves. The first procedure lacks the merit of providing a full general relativistic treatment of the problem. The second relies on very debatable assumptions that lack sound reasons to be trusted throughout the whole spherical collapse process. On the other hand, progresses of numerical relativity over the past decades have allowed to solve for the full relativistic formulation of the problem in the case of an asymptotically flat space-time. In this work, we wish to provide a complete numerical relativistic study of cosmological spherical collapse and discuss the differences in results compared with the traditional treatment.

Title: Gravitational collapse with rotating thin shells and cosmic censorship

The study of gravitational collapse is a subject of great importance, both from an astrophysical and a holographic point of view. In this respect, exact solutions can be very helpful but known solutions are very scarce, especially when considering dynamical processes with rotation. I will identify a setup in which gravitational collapse of rotating matter shells can be addressed with analytic tools, at the expense of going to higher dimensions and considering equal angular momenta spacetimes. The framework for exact and perturbative studies is developed, relying on a thin shell approximation. I will also discuss applications of this machinery to the cosmic censorship conjecture and to constructions of stationary solutions describing matter around rotating black holes.

Title: Non-Riemannian geometry: towards new avenues for the physics of modified gravities

A foundational aspect of classical of classical gravity, namely, whether the underlying structure of space-time is Riemannian or not, has been understimated in the literature due to the sucess of General Relativity, formulated on a Riemannian manifold. In this talk we discuss the consequences that removing any a priori assumption on the relation between metric and connection (metric-affine or Palatini approach) have for the physics of modified gravity in several scenarios such as black holes, cosmology or higher dimensions.

Title: Numerical evolution of Robinson-Trautman spacetimes

Some preliminary results on the time evolution and gravitational recoil in nonsym-metric Robinson-Trautman spacetimes are presented. These results have been obtained by using an efficient full numerical approach based in the Galerkin spectral method to analyze the non-linear regime of the nonsymmetric Robinson-Trautman equations. A good accuracy with modest computational resources has been attained.

Title: Nonlinear r-mode instability in uniformly rotating stars

We have investigated nonlinear r-mode instability in uniformly rotating stars, triggered by gravitational radiation, restored by Coriolis force. We have succeeded in developing and verifying our new code in rotating reference frame by reproducing two representative nonlinear features: saturation amplitude and dynamical destruction of its instability. We have also succeeded in constructing our new computational scheme imposing nonlinear anelastic condition, which essentially kills the propagation effect of accoustic waves. Our new approach enables us to simulate r-mode instability 10 -- 100 times longer than in hydrodynamical approach. Comparison of our results of nonlinear anelastic approximation with those of hydrodynamics will be discussed.

Title: Geometric aspects of charged black holes in Palatini theories.

Charged black holes in gravity theories in the Palatini formalism present a number of unique properties. Their innermost structure is topologically nontrivial, representing a wormhole supported by a sourceless electric flux. For certain values of their effective mass and charge curvature singularities may be absent, and their event horizon may also disappear yielding a remnant. In this talk i will briefly give an overview of the mathematical derivation of these solutions and will discuss their geodesic structure and other geometric properties.

Title: Fully covariant and conformal formulation of the Z4 system in a reference-metric approach in spherical polar coordinates

We have generalized a covariant and conformal version of the Z4 system of the Einstein equations using a reference metric approach, that we denote as the fCCZ4. We have successfully implemented and tested the fCCZ4 in a 1D-code that uses spherical coordinates and assumes spherical symmetry, obtaining one to three orders of magnitude, at least in neutron star space-times, of reduction of the Hamiltonian constraint violations with respect to the BSSN formulation. I will talk about the implementation of the fCCZ4 in a full 3D code using spherical polar coordinates and present the results for some tests we have performed.

Title: Inestabilities in Anti-de Sitter

In the last years, the stability of Anti-de Sitter spacetimes has attracted a lot of attention. Not only because of its own importance but primarily due to the AdS/CFT correspondence that conjectures that exists an equivalence between string theory on an asymptotically AdS spacetime and a conformally invariant quantum ?eld theory (CFT). The result of Bizon and Andrzej Rostworowski (2011) showed that the boundary of AdS prevents energy to disperse and generates a collapse after this energy has bounced in it some number of times. After these years and some related works, the exact mechanisms that triggers the inestability are still a topic of discussion. In our work, we pressent a new approach to this problem that we expect helps to answer some questions.

Title: Spectral approach to axisymmetric evolution of Einstein's equations

In this talk I present a new formulation of the Einstein equations for a non-rotating axisymmetric spacetime in vacuum. The majority of formulations for this situation uses cylindrical polar coordinates. In contrast to those we introduce spherical polar coordinates. A general problem for this choice is the occurrence of a coordinate singularities at the axis of symmetry and at the origin. Spherical harmonics are manifestly regular at the axis and hence take care of that issue automatically. Therefore I spectrally decompose all the variables in the appropriate (tensor) harmonics. I also address the question of an appropriate gauge choice and the regularization of the coordinate singularity at the origin.

Title: Teaching the basics of relativity: lessons from the history and philosophy of science.

Clocks at lower gravitational field potential appear to run more slowly than identical clocks at higher potential. The result follows from a general relativistic effect known as the gravitational redshift, first Einstein proposed in 1907. Early attempts for a clear derivation of the gravitational redshift were fraught with errors and ambiguities, and much confusion endured for the next two decades. This suggests that the subject should be treated carefully in introductory textbooks on relativity theory. I analyze the weaknesses of the presentation in four otherwise excellent modern introductory GR books (by Rindler, Schutz, Hobson et al., and Carroll). I also present some analysis from a history and philosophy of physics article, (Earman and Glymour, 1980), which proves to be a great resource to learn about, anticipate, and clarify problems in teaching the redshift.

Title: Wormhole dynamics in higher-dimensional space-time

The most popular wormhole (Ellis wormhole, so-called Morris-Thorne wormhole) is known to be unstable [HS and Hayward, PRD 66(2002) 044005]. We extend this study in $n$-dimensional spacetime. We derive the solution and check their stability using linear perturbation analysis [Torii and HS, PRD 88(2013) 064027]. We find an unstable mode for any dimension. We also confirm this result with numerical computation with dual-null system. The dynamical behavior of wormholes in Gauss-Bonnet gravity is also planned to be reported.

Title: New Perspectives on Hawking Radiation

The talk will take up the "Hawking effect" for various non-asymptotic observers in a new perspective by considering Unruh-DeWitt detectors moving along nonstationary, nonasymptotic trajectories (in an adiabatic formalism). When applied to geodesic trajectories, this formalism yields the following results: (i) though they have zero acceleration, the temperature measured by detectors on circular orbits is higher than that measured by static detectors at the same distance from the hole, and diverges on the photon sphere, (ii) in the near-horizon region, both outgoing and incoming modes excite infalling detectors, and, for highly bound trajectories, the latter actually dominate the former. The results are confirmed by looking at an alternate probe using the local invariant observables - energy density and flux - which explicitly depend on the kinematics of the concerned observers. Our results show the thermal Tolman-shifted energy density and fluxes for the static observers which diverge at the horizon. We also confirm the apparent perception of high-temperature Hawking radiation by infalling observers with $E\ll1$ by showing that the energy flux measured by these observers diverges in the $E\rightarrow0$ limit. But, for the in-falling observer starting with $r_i>>2M$, both the quantities, energy density and flux at the horizon crossing are regular and finite. For example, the flux at the horizon for the in-falling observer from infinity is approximately 24 times the flux for the observer at infinity. We show that compared with the static observers in the near-horizon region, this is quite small. However, both the quantities, energy density and the flux grow as the in-fall progresses inside the horizon and diverge at the singularity which can have implications in considering the backreaction on the geometry. We also discuss the role played by spacetime curvature on the near-horizon Hawking radiation.

Title: Anisotropic Power-law Inflation

We provide a counter example to the cosmic no-hair conjecture. In particular, we show there are many exact inflationary solutions with anisotropic hair. We also discuss observational consequences of these anisotropic inflation models.

Title: Shocks in the low angular momentum accretion flows

We address the variability of low luminous galactic nuclei including the Sgr A* or other quiescent accreting systems, e.g. the black hole X-ray binaries in their quiescent state, such as V 404 Cygni. These sources exhibit bright X-ray flares and are theoretically interpreted as the quasi-spherical accretion flows, formed instead of an evaporated Keplerian accretion disks. In low angular momentum flows the existence of shocks for some range of leading parameters (energy, angular momentum and adiabatic constant of the gas) was studied semi-analytically. The possible hysteresis effect, caused by the fact that the evolution of the flow and the formation of the shock depends on its own history, was discovered. The presence of the shock in the accreted material is important for the observable properties of the outcoming radiation. In the shocked region the gas is dense and hot, thus much more luminous than in the other case. We study the appearance of standing shocks in low angular momentum gas accretion onto black holes in numerical hydrodynamical simulations using the ZEUS code with Paczynski-Wiita pseudo-Newtonian potential.

Title: What can we learn from gravitational waves from nearby core-collapse supernovae?

Core-collapse supernova is one of the expected sources of gravitational wave (GW). The GW detection can be a smoking gun to probe the still unknown explosion mechanism. In the coming era of "multi-messenger astronomy", we can use photons, neutrinos and GW simultaneously to investigate these objects. By performing multi-dimensional simulations of neutrino-radiation hydrodynamics systematically, we calculate the gravitational wave and neutrino signals from nearby (galactic) core-collapse supernova. Based on these signals we will discuss the extractable information about the very central part of core-collapse supernovae.

Title: Non-perturbative analysis of the Einstein equation in the large D limit

Recent studies have revealed the dynamics of the black hole perturbation can be described by a very simple structure in the large limit of the number of the dimension, the large D limit. In this talk, we will discuss the application of the large D limit to the non-perturbative analysis of the Einstein equation.

Title: Averaging in cosmology based on Cartan scalars

We present a new approach for averaging in general relativity and cosmology. After a short review of the theory originally taken from the equivalence problem, we consider two ways how to deal with averaging based on Cartan scalars. We apply the theory for two different LTB models. In the first one, correlation term behaves as a positive cosmological constant, in the second example leading correlation term behaves like spatial curvature. We also show nontriviality of averaging for linearized monochromatic gravitational wave.

Title: Revisiting the charged BTZ metric in nonlinear electrodynamics

In contrast to its chargeless version the charged Banados,Taitelboim and Zanelli(BTZ) metric in linear Maxwell electromagnetism is known to be singular at r = 0. We show, by employing nonlinear electrodynamics that one obtains charged,extension of the BTZ metric with regular electric field. This we do by choosing a logarithmic Lagrangian for the nonlinear electrodynamics.

Title: Constraining the equation of state of neutron stars from binary mergers

Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we have found that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the compactness of the progenitor stars. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We have tested our approach with simulated data and verified it works well for all the equations of state considered.

Title: Aspects of Large D black holes

General relativity has a spacetime dimension, D, as a dimensionless parameter of theory. We consider the limit of infinite D of GR. Then we find that the gravity structure of black holes become very simple, but its non-triviality is remaining. Using this fascinating features, we discuss the various physical properties of black holes at large D such as quasinormal modes and so on.

Title: Renormalized stress-energy tensor for Dirac fields in expanding universes

We discuss the application of the adiabatic regularization method to the renormalization of the stress-energy tensor for spin-1/2 fields in expanding universes. We first obtain for a Robertson-Walker metric the terms that are necessary to subtract from the bare infinite expression. After that, we apply the method to two interesting cosmological scenarios: i) particle creation in a radiation-dominated universe from vacuum fluctuations, and ii) particle creation in the broad resonance regime of preheating after inflation.

Title: Accretion onto neutron stars and the hidden magnetic field model.

We present 1D and 2D magnetohydrodynamical simulations of the accretion onto neutron stars. We study the consecuences of the accretion of non-magnetized fluid with microphysical equation of state to the magnetosphere of the star. We explore different accretion rates, fluid composition and magnetic field distributions, in order to the test the viability of this scenario. This model has been presented as a viable scenario to explain the evolution of X-ray sources with low values (less than $10^11$ G) of magnetic field. In this scenario, the matter of the reverse shock falling back to the compact object, a neutron star, compress star magnetic field, which can be eventually buried at neutron star crust.

Title: Unconstrained hyperboloidal evolution of strong field initial data in spherical symmetry

We consider unconstrained evolution schemes for the hyperboloidal initial value problem in numerical relativity as a promising candidate for the optimally efficient numerical treatment of radiating compact objects. Here, spherical symmetry already poses nontrivial problems and constitutes an important first step to regularize the resulting singular PDEs. We evolve the Einstein equations in their Generalized BSSN and Z4 formulations coupled to a massless self-gravitating scalar field. Stable numerical evolutions are achieved both for globally regular and black hole initial data, and critically rely on the construction of appropriate gauge conditions.

Title: The dynamics of nonmetricity in metric-affine theories of gravity

Adopting a procedure borrowed from the effective field theory prescriptions, we will review the dynamics of metric-affine theories of increasing order, that in the complete version include invariants built from curvature, nonmetricity and torsion. We show that even including terms obtained from nonmetricity and torsion to the second order density Lagrangian, the connection lacks dynamics and acts as an auxiliary field that can be algebraically eliminated, resulting in some extra interactions between metric and matter fields.

Title: Gravity as a theory of curved surface dynamics

We consider a class of isometric embeddings which are perturbable, in the sense that they allow one to encode all the local degrees of freedom of General Relativity. We show that GR can be formulated as a nonlinear hyperbolic system (wave equation) for embedding coordinates, and suggest some physical applications and open problems.

Title: Hamiltonian Reduction of Einstein's Equations in the (2+2) Formalism

I describe in detail the procedure of Hamiltonian reduction of general relativity of 4 dimensional spacetimes under no symmetry assumptions using the (2+2) formalism. The privileged spacetime coordinates are such that the physical time is the {\it area} element of the spatial cross section of out-going null hypersurfaces, and the physical radial coordinate is defined by {\it equipotential} surfaces on a given spacelike hypersurface of constant physical time. In the privileged coordinates, the Einstein's constraints are completely solved to determine the non-zero physical Hamiltonian and momentum densities in terms of the physical degrees of freedom of gravitational field, which are the conformal two metric and its conjugate momentum. The physical degrees of freedom are not free but subject to a topological constraint that dictates the spatial topology of a compact two dimensional cross section of a null hypersurface be either a two sphere or a torus. The physical Hamiltonian is local, and has an explicit dependence on the physical time. I present Hamilton's equations of motion which follow from the non-zero physical Hamiltonian, and find that they are identical to Einstein's equations written in the privileged coordinates. This proves that the Hamiltonian reduction proposed in this paper is a self-consistent procedure. As an application of the Hamiltonian reduction, I present three exact solutions, i.e. the Minkowski spacetime, the plane symmetric solution of Taub, and the general Kasner solution by solving Hamilton's equations of motion governed by the physical Hamiltonian. This work may be regarded as a generalization of the ADM Hamiltonian reduction of midi-superspace to 4 dimensional spacetimes with no isometries.

Title: Cosmological expansion using a relativistic extended description of gravity.

A large number of modified non-relativistic and relativistic theories of gravity have been constructed in order to avoid dark and/or energy entities. The relativistic metric extension $f(\chi)$ by Bernal et al. (2012) has shown to be useful at galactic and extragalactic scales. Carranza et al. (2013) showed that this extension of gravity is capable of explaining the current accelerated expansion of the Universe. This approach is not complete and the appearance of a mass in the gravitational action yields immediate problems with further generalisations. In this talk I will show how a more effective extended metric theory of gravity $f(\chi)$ can be constructed by taking into account point mass sources generating the gravitational field and with it, I will show that this description can account for the observed accelerated expansion of the Universe without the need to introduce dark entities in the description of gravitational phenomena.

Title: Regular and Chaotic Motion in General Relativity: The Case of a Massive Magnetic Dipole

Circular motion of particles, dust grains and fluids in the vicinity of compact objects has been investigated as a model for accretion of gaseous and dusty environment. Here we further discuss, within the framework of general relativity, figures of equilibrium of matter under the influence of combined gravitational and large-scale magnetic fields, assuming that the accreted material acquires a small electric charge due to interplay of plasma processes and photoionization. In particular, we employ an exact solution describing the massive magnetic dipole and we identify the regions of stable motion. We also investigate situations when the particle dynamics exhibits the onset of chaos. In order to characterize the measure of chaoticness we employ techniques of Poincar\'e surfaces of section and of recurrence plots.