An Axisymmetric Gravitational Collapse Code

TL;DR

This paper introduces a new numerical code for simulating axisymmetric spacetimes in general relativity, enabling studies of gravitational collapse, black hole collisions, and cosmic censorship with stable evolution techniques.

Contribution

It develops a (2+1)+1 formalism and numerical methods that achieve stable evolution of axisymmetric Einstein equations, handling singularities and regularity conditions.

Findings

Achieved stable numerical evolution of axisymmetric spacetimes.

Successfully handled singularities at the axis through regularity conditions.

Demonstrated the code's potential for studying gravitational collapse and black hole interactions.

Abstract

We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry, including gravitational collapse, critical phenomena, investigations of cosmic censorship, and head-on black hole collisions. Our objective here is to detail the (2+1)+1 formalism we use to arrive at the corresponding system of equations and the numerical methods we use to solve them. We are able to obtain stable evolution, despite the singular nature of the coordinate system on the axis, by enforcing appropriate regularity conditions on all variables and by adding numerical dissipation to hyperbolic equations.