Testing a Simplified Version of Einstein's Equations for Numerical Relativity

TL;DR

This paper evaluates a simplified approximation scheme for Einstein's equations in numerical relativity by testing it on isolated, rapidly rotating relativistic stars to assess its accuracy near equilibrium conditions.

Contribution

It introduces and tests a simplified, approximate scheme for Einstein's equations applicable to near-equilibrium systems in numerical relativity.

Findings

The approximation performs well on isolated, rapidly rotating relativistic stars.

Results are promising for the scheme's use in more complex systems like binary neutron stars.

The study supports the scheme's potential for simplifying numerical relativity calculations.

Abstract

Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on isolated, rapidly rotating, relativistic stars. Since these objects are in equilibrium, it is crucial that the approximation work well if we are to believe its predictions for more complicated systems like binaries. Our results are very encouraging.