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dc.contributor.authorVan de Moortel, Maxime Claude Robert
dc.date.accessioned2019-05-07T10:14:09Z
dc.date.available2019-05-07T10:14:09Z
dc.date.issued2019-05-18
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/292445
dc.description.abstractThe goal of this thesis is to study charged Black Holes in the presence of charged matter. To do so, we investigate the behaviour of spherically symmetric solutions of the Einstein-Maxwell-Klein-Gordon equations, which model the interaction of a charged scalar field with the electromagnetic field originating from the Black Hole charge. The particularity of this model is to putatively admit charged one-ended Black holes with a Cauchy horizon, and thus provides a framework to study simultaneously charged gravitational collapse and the Strong Cosmic Censorship conjecture. The latter problem is related to the question of Determinism of General Relativity, and roughly states that the maximal development of admissible initial data is inextendible. This question is intimately connected to the geometry of the Black Hole interior, which is studied in the first chapter of the present thesis. We prove that perturbed charged Black Holes form a Cauchy horizon which admits generically a singularity. This singularity in turn forms an obstruction to extending the maximal development. To obtain this result, we undertake an asymptotic analysis of the scalar field in the interior of the Black Hole, assuming its exterior region settles towards a stationary solution at a time decay rate that is expected by numeric and heuristic works. In the second chapter of this thesis, we retrieve these time decay rates for weakly charged scalar field on a fixed Reissner-Nordstrom Black Hole exterior. The result provides a proof of the (gravity-uncoupled) stability of Reissner-Nordstrom Black Hole exterior against small charged perturbations, which should also be considered as the first step towards the construction of one-ended charged Black Holes with a Cauchy horizon.
dc.description.sponsorshipK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1.
dc.language.isoen
dc.rightsAll rights reserved
dc.rightsAll Rights Reserveden
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/en
dc.subjectStrong Cosmic Censorship
dc.subjectBlack Hole interior
dc.subjectReissner-Nordstrom
dc.subjectCharged scalar field
dc.subjectKlein-Gordon
dc.subjectCauchy horizon
dc.titleCharged scalar fields on Black Hole space-times
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.publisher.departmentDPMMS
dc.date.updated2019-05-07T09:09:41Z
dc.identifier.doi10.17863/CAM.39604
dc.publisher.collegeRobinson Collegr
dc.type.qualificationtitlePhD in Pure Mathematics
cam.supervisorLuk, Jonathan
cam.thesis.fundingtrue


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