Regularization of spherically symmetric evolution codes in numerical relativity

TL;DR

This paper introduces a versatile algorithm for regularizing spherically symmetric evolution equations in numerical relativity, improving stability and applicability across various gauge choices and formulations.

Contribution

A general regularization algorithm for spherically symmetric evolution codes that can be applied directly to evolution equations and is compatible with diverse gauge conditions.

Findings

Algorithm effectively regularizes variables at the origin.

Applicable to a wide range of evolution systems.

Enhances stability of numerical relativity simulations.

Abstract

The lack of regularity of geometric variables at the origin is often a source of serious problem for spherically symmetric evolution codes in numerical relativity. One usually deals with this by restricting the gauge and solving the hamiltonian constraint for the metric. Here we present a generic algorithm for dealing with the regularization of the origin that can be used directly on the evolution equations and that allows very general gauge choices. Our approach is similar in spirit to the one introduced by Arbona and Bona for the particular case of the Bona-Masso formulation. However, our algorithm is more general and can be used with a wide variety of evolution systems.