Quantifying closeness between black hole spacetimes: a superspace approach

• Published in: arXiv.org
• Main Author: Suvorov, Arthur G
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 20.07.2020
• Subjects: Exact solutions; Manifolds (mathematics); Mathematics - Mathematical Physics; Physics - General Relativity and Quantum Cosmology; Physics - High Energy Astrophysical Phenomena; Physics - Mathematical Physics; Relativity; Riemann manifold
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2007.08070

The set of all metrics that can be placed on a given manifold defines an infinite-dimensional `superspace' that can itself be imbued with the structure of a Riemannian manifold. Geodesic distances between points on Met\((M)\) measure how close two different metrics over \(M\) are to one another. Restricting our attention to only those metrics that describe physical black holes, these distances may therefore be thought of as measuring the level of geometric similarity between different black hole structures. This allows for a systematic quantification of the extent to which a black hole, possibly arising as an exact solution to a theory of gravity extending general relativity in some way, might be `non-Kerr'. In this paper, a detailed construction of a superspace for stationary black holes with an arbitrary number of hairs is carried out. As an example application, we are able to strengthen a recent claim made by Konoplya and Zhidenko about which deviation parameters describing a hypothetical, non-Schwarzschild black hole are likely to be most relevant for astrophysical observables.