Discrete differential forms for cosmological space-times

TL;DR

This paper explores the use of discrete differential forms in numerical general relativity, demonstrating their effectiveness and stability in simulating vacuum space-times with gravitational waves, especially using the Gowdy solution as a test case.

Contribution

It introduces and tests a discrete differential form method for simulating cosmological space-times, showing its accuracy, stability, and coordinate independence in complex scenarios.

Findings

Accurate reproduction of the Gowdy solution

Stable long-term numerical evolution

Quadratic convergence of the scheme

Abstract

In this article we describe applications of the numerical method of discrete differential forms in computational GR. In particular we consider the initial value problem for vacuum space-times that admit plane gravitational waves. As described in an earlier paper the discrete differential form approach can provide accurate results in spherically symmetric space-times. Moreover it is manifestly coordinate independent. Here we use the polarised Gowdy solution as a testbed for two numerical schemes. One scheme reproduces that solution very well, in particular it is stable for a comparatively long time and converges quadratically.