Scientific activity developed within the PROMETHEUS project can be systematized in the following sections:

- relativistic jets:

• relativistic jets in AGNs
• relativistic jets in microquasars
• Winds progenitors relativistic gamma-ray bursts

- astrophysical sources of gravitational radiation:

• Torus accretion on compact objects magnetized neutron star rotated
• magneto-rotational stellar collapse

- Computational Relativity: formalism of the Einstein equations

- Computational Cosmology: Galaxies and clusters of galaxies.

1. Accretion onto compact objects
   We will compute the gravitational radiation from thick accretion disks around Kerr black holes. Self-gravity and magnetic fields will be accounted for. We will also compute the gravitational radiation produced in the excitation of quasi-normal modes of oscillation of neutron stars and black holes as a result of accretion events.
   
   
2. Stellar collapse
   A parameter study of axisymmetric relativistic (magneto-)rotational stellar core collapse will be performed. Both, collapse dynamics and gravitational radiation waveforms will be analyzed, uisng different formulations for Einstein's equations (CFC, characteristic, and full-constrained). A three-dimensional code will be developed to perform magneto-rotational core collapse simulations to neutron stars and black holes. This code will also be used to study the evolution of dynamical instabilities in rapidly-rotating neutron stars.
   
   
3. Pulsations of neutron stars
   The frequency spectra of differentially rotating relativistic stars and the associated gravitational radiation will be studied, including non-adiabatic effects and the influence of the equation of state thereof. We will build equilibrium initial models of magnetized and rotating relativistic stars. Normal modes of pulsation associated with the fluid and with the magnetic field will be investigated.
   
   
4. Magnetized neutron stars
   We intend to study the physical processes taking place in magnetized neutron stars to better understand recent observations of Isolated Neutron Stars and magnetars in which the presence of a strong magnetic field plays a crucial role on the thermal structure and evolution of the star. In particular, we plan to obtain the magneto-thermal structure and evolution of these objects and by comparison with observations to fit the parameters of our models. The effect of the magnetic field on the pulsations of the neutron star will be also studied in the linear approximation, to obtain the gravitational and electromagnetic emission of pulsating magnetized neutron stars.
   
   
5. Evolution of rotating protoneutron stars
   We plan to study the evolution of rotating protoneutron stars taking into account the asphericity caused by rotation. To this end, we will develop a 3D neutrino transport code based on spectral methods, coupled to a hydo code in the inelastic approximation.
   
   
6. Relativistic jets in active galaxies
   We intend to obtain a better understanding of the nature of the relativistic jets commonly present in active galaxies. In particular, we plan to study the importance of the magnetic field in the jet dynamics and observed emission, the processes that govern the jet formation, collimation, acceleration and emission in the innermost regions, and the origin of the commonly observed jet precession. At larger scales we plan to focuss on the origin of the morphological FRI-FRII dichotomy.
   
   
7. Kelvin-Helmholtz instabilities in relativistic magnetized flows
   We plan to extend the study of Kelvin-Helmholtz instabilities to relativistic magnetized flows, in three spatial dimensions, with general equations of state and plasma compositions.
   
   
8. Gamma-Ray Bursts (GRB)
   The formation of ultrarelativistic flows in GRB progenitors and their long term evolution (afterglow phase) will be explored by means of GRMHD simulations and realistic microphysics.