Junctions and thin shells in general relativity using computer algebra I: The Darmois-Israel Formalism

TL;DR

The paper introduces the GRjunction software package for analyzing boundary surfaces and thin shells in general relativity, demonstrating its capabilities through literature examples and a novel Kerr solution junction in the slow rotation limit.

Contribution

It presents a new computer algebra package, GRjunction, for studying thin shells in general relativity, including a novel application to Kerr solution junctions.

Findings

Successfully reproduces literature examples

Verifies the package's correctness

Performs a new Kerr solution junction calculation

Abstract

We present the GRjunction package which allows boundary surfaces and thin-shells in general relativity to be studied with a computer algebra system. Implementing the Darmois-Israel thin shell formalism requires a careful selection of definitions and algorithms to ensure that results are generated in a straight-forward way. We have used the package to correctly reproduce a wide variety of examples from the literature. We present several of these verifications as a means of demonstrating the packages capabilities. We then use GRjunction to perform a new calculation - joining two Kerr solutions with differing masses and angular momenta along a thin shell in the slow rotation limit.