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Título/Title: Palatini f(R) and Extended Palatini f(R,Q) Black Holes with Electric charge.

Autor/Author: Diego Rubiera-García (Universidad de Oviedo )

Abstract: We study electrically charged black holes in f(R) and f(R,Q) theories formulated à la Palatini, i.e. by assuming the metric and connection to be independent entities. We show that in the f(R) case, electromagnetic theories with vanishing trace (as Maxwell theory) itself produces the same equations of motion as those of General Relativity (GR), which motivates us to consider non-linear extensions (non-linear electrodynamics). We show how the structure of GR-Born-Infeld black holes is modified near the center in terms of internal horizons and how the central singularities could be ameliorated. In the f(R,Q) we show that Maxwell theory already produces different results from those of GR, and we find different kinds of structures including regular black holes (singularity-free) and regular cores.

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Título/Title: Quadratic deformation of Minkowski and conformal spaces

Autor/Author: Dalia Cervantes (Universidad Nacional Autónoma de México )

Abstract: We give a deformation of Minkowski space which is both, algebraic and differential, and that can be extended to the conformal space by preserving an action of the quantum conformal group. The Poisson bracket is quadratic in Minkowski's coordinates.

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Título/Title: Non-linear electrodynamics in gravity: basics and some applications.

Autor/Author: Diego Rubiera-García (LUTH, Observatoire de Paris-Meudon, Francia)

Abstract: The Reissner-Nordström black hole describes the gravitational and electromagnetic fields created by a spherically symmetric object governed by two parameters: its mass and electric charge. Generalizations of this solution through non-linear electrodynamics and their non-abelian generalizations have received a considerable interest in the last decades. In this talk I will give an overview of the current state of the topic and describe my own contributions to it. In particular, I shall describe a general procedure which allows to classify and qualitatively characterize the whole family of non-linear electrodynamics defined as arbitrary functions of the two field invariants and satisfying certain requirements for physical consistence of the theories. Through this procedure it is possible to study several features of the black holes including its metric structure and thermodynamics without explicitly fixing the lagrangian density function. Some explicit examples are given. Finally I will describe applications of this method to other interesting cases, such as generalized non-abelian gauge fields, and to other gravity theories such as the Lovelock one.

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Título/Title: Unifying Einstein and Palatini gravities

Autor/Author: Tomi Koivisto (Institute for Theoretical Physics and Spinoza Institute, Utrecht University )

Abstract: I present a new approach to nonmetric theories of gravity. There the relation of the metric and the connection can have a nontrivial a priori dependence upon the curvature. As an example, I consider a conformal relation. The corresponding action then describes Einstein and Palatini f(R) theories at special limits, and contains new inter- and extrapolating theories which avoid some pathologies of especially the Palatini f(R) case. I outline how the approach can be applied for more general than conformal relations, to generalize Einstein and Palatini versions of theories involving arbitrary curvature invariants in the action.

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