The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge
File(s)
Author(s)
Johnson, Thomas William
Type
Thesis
Abstract
We prove in this thesis that the Schwarzschild family of black holes are linearly stable as solutions to the Einstein vacuum equations as expressed in a generalised wave gauge: all sufficiently regular solutions to the system of equations that result from linearising the Einstein vacuum equations, as expressed in a generalised wave gauge, about a fixed Schwarzschild solution remain uniformly bounded on the Schwarzschild exterior region and in fact decay to a member of the linearised Kerr family. The dispersion is at an inverse polynomial rate and therefore in principle sufficient for future nonlinear applications. The result thus fits into the wider goal of establishing the full nonlinear stability of the exterior Kerr family as solutions to the Einstein vacuum equations by employing a generalised wave gauge.
Version
Open Access
Date Issued
2018-05
Date Awarded
2018-07
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Holzegel, Gustav
Sponsor
European Research Council
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)