General Relativistic Hydrodynamics with Special Relativistic Riemann Solvers

TL;DR

This paper introduces a practical method for solving general relativistic hydrodynamics equations by locally transforming the spacetime metric to Minkowskian form, enabling the use of existing special relativistic Riemann solvers with minimal additional computational cost.

Contribution

The authors propose a local coordinate transformation technique that allows the application of special relativistic Riemann solvers to general relativistic hydrodynamics problems, simplifying computations.

Findings

Method confirmed through numerical experiments

Accurate results with negligible computational overhead

Applicable to a wide range of general relativistic flows

Abstract

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 of general relativistic hydrodynamics problems using the numerical tools developed for the special relativistic case with negligible computational cost. The feasibility of the method has been confirmed by a number of numerical experiments.