The wave equation on black rings and the linear stability of slowly rotating Kerr spacetimes
File(s)
Author(s)
Benomio, Gabriele
Type
Thesis
Abstract
The existence of black holes is perhaps the most spectacular prediction of Einstein's classical theory of general relativity. Recent advances in both theoretical and experimental physics, such as the discovery of gravitational waves, have confirmed that black holes are stable, macroscopic objects playing a fundamental role in our universe. On the other hand, modern physical theories demand for a higher dimensional formulation of general relativity, and thus to understand the stability properties of black holes within a wider scenario than the one directly probed by the astrophysical observations. However, the mathematical question of whether black holes are stale as solutions to the vacuum Einstein equations Ric(g)=0, known as the black hole stability problem, remains, to large extent, open. The present thesis contributes to the black hole stability problem with two theorems. Chapter 2 of the thesis considers a family of higher dimensional black holes, known as black rings. The potential stability of this family, and the part that physical theories should reserve to them if unstable, have been largely investigated in the physics literature. The main theorem of the chapter is the first mathematically rigorous result suggesting that these black holes are unstable to gravitational perturbations. In particular, we establish a logarithmic lower bound for the uniform energy decay rate of scalar linear perturbations on black ring spacetimes. Chapter 3 of the thesis deals with the Kerr family of black holes, which is believed to characterise all the astrophysical stationary black holes. To agree with our physical expectation, the Kerr stability conjecture claims that these black holes are stable to gravitational perturbations. The content of the chapter represents the first part of work by the author providing the last missing ingredient towards a final proof of the conjecture for the slowly rotating members of the Kerr family. More precisely, we formulate the problem of linear stability of Kerr black holes to gravitational perturbations in a new geometric gauge.
Version
Open Access
Date Issued
2020-08
Date Awarded
2020-10
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
Advisor
Holzegel, Gustav
Warnick, Claude
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)