Application of Discrete Differential Forms to Spherically Symmetric Systems in General Relativity

TL;DR

This paper explores the use of Discrete Differential Forms in computational general relativity, focusing on spherically symmetric vacuum space-times, demonstrating coordinate-independent schemes with quadratic convergence.

Contribution

It introduces three numerical schemes based on Discrete Differential Forms for spherically symmetric systems in GR, highlighting their convergence and dependence on initial data.

Findings

Two schemes exhibit quadratic error convergence.

Errors in one scheme depend strongly on initial data.

Coordinate independence of the methods is demonstrated.

Abstract

In this article we describe applications of Discrete Differential Forms in computational GR. In particular we consider the initial value problem in vacuum space-times that are spherically symmetric. The motivation to investigate this method is mainly its manifest coordinate independence. Three numerical schemes are introduced, the results of which are compared with the corresponding analytic solutions. The error of two schemes converges quadratically to zero. For one scheme the errors depend strongly on the initial data.