On the stability of covariant BSSN formulation

TL;DR

This paper analyzes the numerical stability of the covariant BSSN formulation in numerical relativity by examining the constraint amplification factor, showing that adjusted formulations with added constraints are more stable.

Contribution

It provides a stability analysis of the covariant BSSN formulation and introduces adjusted formulations with improved numerical stability based on CAF analysis.

Findings

Adjusted formulations exhibit higher stability than cBSSN.

Constraint amplification factors are used to evaluate stability.

Adjusted formulations could enhance numerical relativity simulations.

Abstract

In this study, we investigate the numerical stability of the covariant BSSN (cBSSN) formulation proposed by Brown. We calculate the constraint amplification factor (CAF), which is an eigenvalue of the coefficient matrix of the evolution equations of the constraints on the cBSSN formulation and on some adjusted formulations with constraints added to the evolution equations. The adjusted formulations have a higher numerical stability than the cBSSN formulation from the viewpoint of the CAF.