Exploration of General Relativistic Hydrodynamics for FRW Metric

General relativistic hydrodynamics with a Roe solver

We present a numerical method to solve the equations of general relativistic hydrodynamics in a given external gravitational field. The method is based on a generalization of Roe’s approximate Riemann solver for the non relativistic Euler equations in Cartesian coordinates. The new method is applied to a set of standard test problems for general relativistic hydrodynamics, and is shown to perfo...

General relativistic hydrodynamics and magnetohydrodynamics: hyperbolic systems 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 ...

Equations of general relativistic radiation hydrodynamics in Kerr space - time

Equations of fully general relativistic radiation hydrodynamics in Kerr space-time are derived. While the interactions between matter and radiation are introduced in the comoving frame, the derivatives used when describing the global evolutions of both the matter and the radiation are given in the Boyer-Lindquist frame (BLF) which is a frame fixed to the coordinate describing the central black ...

Special relativistic spherically symmetric Lagrangean hydrodynamics from General Relativity

We re-derive hydrodynamical equations in General Relativity (GR) in the comoving reference frame for spherical symmetry and obtain from them the well-known but not explicitly derived Lagrangean equations in Special Relativity (SR), that is, for the case of weak gravitational fields. Explicit formulae are presented which relate General Relativistic independent variables, Lagrangean mass coordina...