Spectral methods in general relativistic astrophysics

General relativistic hydrodynamics and magnetohydrodynamics: hyperbolic systems in relativistic astrophysics

Conformal Mappings in Relativistic Astrophysics

We describe the use of conformalmappings as amathematicalmechanism to obtain exact solutions of the Einstein field equations in general relativity. The behaviour of the spacetime geometry quantities is given under a conformal transformation, and the Einstein field equations are exhibited for a perfect fluid distribution matter configuration. The field equations are simplified and then exact sta...

Relativistic Astrophysics Explorer

The great success of the Rossi X-Ray Timing Explorer (RXTE) has shown that X-ray timing is an excellent tool for the study of strong gravitational fields and the measurement of fundamental physical properties of black holes and neutron stars. Here, we describe a next-generation X-ray timing mission, the Relativistic Astrophysics Explorer (RAE), designed to fit within the envelope of a medium-si...

Formulation of discontinuous Galerkin methods for relativistic astrophysics

The DG algorithm is a powerful method for solving pdes, especially for evolution equations in conservation form. Since the algorithm involves integration over volume elements, it is not immediately obvious that it will generalize easily to arbitrary time-dependent curved spacetimes. We show how to formulate the algorithm in such spacetimes for applications in relativistic astrophysics. We also ...

ar X iv : g r - qc / 9 81 10 89 v 1 2 6 N ov 1 99 8 Spectral methods in general relativistic astrophysics

We present spectral methods developed in our group to solve three-dimensional partial differential equations. The emphasis is put on equations arising from astro-physical problems in the framework of general relativity.