Application of discrete differential forms to spherically symmetric systems in general relativity

Abstract

In this paper we describe applications of discrete differential forms in computational GR. In particular we consider the initial value problem in vacuum spacetimes 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. © 2007 IOP Publishing Ltd.