Riemann solvers in relativistic astrophysics

General relativistic hydrodynamics with special relativistic Riemann solvers

We present a general and practical procedure to solve the general relativistic hydrodynamic equations by using any of the special relativistic Riemann solvers recently developed for describing the evolution of special relativistic flows. Our proposal relies on a local change of coordinates in terms of which the spacetime metric is locally Minkowskian and permits accurate numerical calculations ...

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...

Nonclassical Riemann solvers with nucleation

We introduce a new nonclassical Riemann solver for scalar conservation laws with concave-convex flux-function. This solver is based on both a kinetic relation, which determines the propagation speed of (undercompressive) nonclassical shock waves, and a nucleation criterion, which makes a choice between a classical Riemann solution and a nonclassical one. We establish the existence of (nonclassi...

General relativistic hydrodynamics and magnetohydrodynamics: hyperbolic systems in relativistic astrophysics