Stable numerical simulation of Einstein equations in gravitational collapse space--time

TL;DR

This paper presents a stable numerical simulation method for Einstein equations in gravitational collapse, incorporating a modified system to reduce errors and successfully simulate nonvacuum scenarios.

Contribution

It introduces a modified formulation of the Einstein and matter equations that enhances stability and accuracy in gravitational collapse simulations.

Findings

Successful stable simulations with reduced numerical errors

Effective handling of nonvacuum gravitational collapse scenarios

Review of BSSN formulation and matter evolution equations

Abstract

We perform simulations in a gravitational collapsing model using the Einstein equations. In this paper, we review the equations for constructing the initial values and the evolution form of the Einstein equations called the BSSN formulation. In addition, since we treat a nonvacuum case, we review the evolution equations of the matter fields of a perfect fluid. To make the simulations stable, we propose a modified system, which decreases numerical errors in analysis, and we actually perform stable simulations with decreased numerical errors.