Conformal geodesics and the evolution of spacetimes with positive Cosmological constant
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 Class. Quantum Grav. 38 145026 and Class. Quantum Grav. 40 145005.
Keywords
Cite
@article{arxiv.2308.04692,
title = {Conformal geodesics and the evolution of spacetimes with positive Cosmological constant},
author = {Marica Minucci},
journal= {arXiv preprint arXiv:2308.04692},
year = {2023}
}
Comments
23 pages, 4 figures. Submitted to Philosophical Transactions A issue: "At the interface of asymptotics, conformal methods and analysis in general relativity". arXiv admin note: substantial text overlap with arXiv:2302.04004