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dc.contributor.advisorDafermos, Mihalis
dc.contributor.authorCivin, Damon
dc.date.accessioned2015-04-21T08:37:54Z
dc.date.available2015-04-21T08:37:54Z
dc.date.issued2015-03-03
dc.identifier.otherPhD.38392
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/247397
dc.description.abstractIn this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay (ILED) results are proved for solutions of the wave equation on the domain of outer communications. The main obstacles to the proof of these results are superradiance, trapping and their interaction. These difficulties are surmounted by localising solutions of the wave equation in phase space and applying the vector field method. Miraculously, as in the Kerr case, superradiance and trapping occur in disjoint regions of phase space and can be dealt with individually. Trapping is a high frequency obstruction to the proof whereas superradiance occurs at both high and low frequencies. The construction of energy currents for superradiant frequencies gives rise to an unfavourable boundary term. In the high frequency regime, this boundary term is controlled by exploiting the presence of a large parameter. For low superradiant frequencies, no such parameter is available. This difficulty is overcome by proving quantitative versions of mode stability type results. The mode stability result on the real axis is then applied to prove integrated local energy decay for solutions of the wave equation restricted to a bounded frequency regime. The (ILED) statement is necessarily degenerate due to the trapping effect. This implies that a nondegenerate (ILED) statement must lose differentiability. If one uses an (ILED) result that loses differentiability to prove (NEB), this loss is passed onto the (NEB) statement as well. Here, the geometry of the subextremal Kerr-Newman background is exploited to obtain the (NEB) statement directly from the degenerate (ILED) with no loss of differentiability.en
dc.description.sponsorshipI acknowledge essential financial support from the Engineering and Physical Sciences Research Council grant EP/H023348/1, the Cambridge Commonwealth Trust, the Cambridge Centre for Analysis and Sidney Sussex College.en
dc.language.isoenen
dc.subjectBlack hole stabilityen
dc.subjectEinstein equationsen
dc.subjectGeneral relativityen
dc.subjectGeometric analysisen
dc.subjectwave equationen
dc.subjectsuperradianceen
dc.subjecttrappingen
dc.subjectKerr-Newmanen
dc.subjectIntegrated local energy decayen
dc.subjectNon degenerate energy boundsen
dc.titleStability of charged rotating black holes for linear scalar perturbationsen
dc.typeThesisen
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridgeen
dc.publisher.departmentDepartment of Pure Mathematics and Mathematical Statisticsen
dc.publisher.departmentCambridge Centre for Analysisen
dc.identifier.doi10.17863/CAM.16236


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