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Title: The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge
Author: Johnson, Thomas William
ISNI:       0000 0004 7427 7539
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2018
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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.
Supervisor: Holzegel, Gustav Sponsor: European Research Council ; Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral