Evolving relativistic fluid spacetimes using pseudospectral methods and finite differencing

TL;DR

This paper introduces a novel computational approach combining pseudospectral methods and finite differencing to simulate relativistic fluid spacetimes governed by Einstein-hydrodynamics equations.

Contribution

It develops a new code that integrates pseudospectral and finite difference techniques for evolving self-gravitating fluids in relativistic spacetimes, with detailed implementation and testing.

Findings

Successful implementation of coupled grid evolution

Effective handling of stellar surfaces

Validated code through tests

Abstract

We present a new code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved on one grid using pseudospectral methods, while the fluids are evolved on another grid by finite differencing. We discuss implementation details, such as the communication between the grids and the treatment of stellar surfaces, and present code tests.