Charged scalar fields on Black Hole space-times

The 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.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2019

Author dc:creator

• Van de Moortel, Maxime Claude Robert

Advisor dc:contributor.advisor

• Luk, Jonathan

• Strong Cosmic Censorship
• Black Hole interior
• Reissner-Nordstrom
• Charged scalar field
• Klein-Gordon
• Cauchy horizon

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/1f54fa89-91f5-43da-acf6-739852914cd3/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

en

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.39604

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/292445