Affiliation:
1. School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
Abstract
This article provides a discussion on the construction of conformal Gaussian gauge systems to study the evolution of solutions to the Einstein field equations with positive Cosmological constant. This is done by means of a gauge based on the properties of conformal geodesics. The use of this gauge, combined with the extended conformal Einstein field equations, yields evolution equations in the form of a symmetric hyperbolic system for which standard Cauchy stability results can be employed. This strategy is used to study the global properties of de Sitter-like spacetimes with constant negative scalar curvature. It is then adapted to study the evolution of the Schwarzschild–de Sitter spacetime in the static region near the conformal boundary. This review is based on Minucci
et al
. 2021
Class. Quantum Grav
.
38
, 145026. (
doi:10.1088/1361-6382/ac0356
) and Minucci
et al
. 2023
Class. Quantum Grav
.
40
, 145005. (
doi:10.1088/1361-6382/acdb3f
).
This article is part of a discussion meeting issue ‘At the interface of asymptotics, conformal methods and analysis in general relativity’.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
1 articles.
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1. At the interface of asymptotics, conformal methods and analysis in general relativity;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2024-01-15