Implementing fully relativistic hydrodynamics in three dimensions

TL;DR

This paper presents a three-dimensional numerical implementation of fully relativistic hydrodynamics coupled with Einstein's equations, demonstrating its effectiveness through tests on equilibrium stars.

Contribution

The paper introduces a new 3D code for relativistic hydrodynamics coupled with Einstein's equations, including recasting of equations and initial testing.

Findings

Successful simulation of stable and unstable Oppenheimer-Volkov stars

Demonstrated advantages of the new code for numerical integration

First promising tests of the coupled relativistic hydrodynamics and Einstein's equations

Abstract

We report on our numerical implementation of fully relativistic hydrodynamics coupled to Einstein's field equations in three spatial dimensions. We briefly review several steps in our code development, including our recasting of Einstein's equations and several tests which demonstrate its advantages for numerical integrations. We outline our implementation of relativistic hydrodynamics, and present numerical results for the evolution of both stable and unstable Oppenheimer-Volkov equilibrium stars, which represent a very promising first test of our code.