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dc.contributor.authorCook, William
dc.date.accessioned2018-07-02T13:56:59Z
dc.date.available2018-07-02T13:56:59Z
dc.date.issued2018-07-20
dc.date.submitted2018-05-14
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/277718
dc.description.abstractThe study of general relativity in higher dimensions has proven to be a fruitful avenue of research, revealing new applications of the theory, for instance in understanding strongly coupled quantum field theories through the holographic principle, and proposing an explanation of the hierarchy problem through TeV gravity scenarios. To understand the non-linear regime of higher dimensional general relativity, such as that involved in the merger of black holes, we use numerical relativity to solve the Einstein equations. In this thesis we develop and demonstrate several diagnostic tools and new initial data for use in numerical relativity simulations of higher dimensional spacetimes, and use these to investigate binary black hole systems. Firstly, we present a formalism for calculating the gravitational waves in a numerical simulation of a higher dimensional spacetime, and apply this formalism to the example of the head on merger of two equal mass black holes. In doing so, we simulate the merger of black holes in up to 10 spacetime dimensions for the first time, and investigate the dependence of the energy radiated away in gravitational waves on the number of dimensions. We also apply this formalism to the example of head on unequal mass black hole collisions, investigating the dependence of radiated energy and momentum on the number of dimensions and the mass ratio. This study complements and sheds further light on previous work on the merger of point particles with black holes in higher dimensions, and presents evidence for a link between the regime studied, and the large $D$ regime of general relativity where $D$ is the number of spacetime dimensions. We also present initial data that enables us to study black holes with initial momentum and angular momentum, putting in place the framework needed to study problems such as the scattering cross section of black holes in higher dimensions, and the nature of black hole orbits in higher dimensions. Finally, we present, and demonstrate the use of, an apparent horizon finder for higher dimensional spacetimes. This allows us to calculate a black hole's mass and spin, which characterise the black hole.
dc.description.sponsorshipDuring the Ph.D. I was supported by an STFC studentship. The numerical work presented in this thesis was performed on DiRAC?s Cosmos Shared Memory system through BIS Grant No. ST/J005673/1 and STFC Grant Nos. ST/H008586/1, ST/K00333X/1, and MareNostrum at Barcelona Supercomputing Center (BSC), Spain under PRACE Grant No. 2016163948. I was also supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska Curie Grant Agreement No. 690904.
dc.language.isoen
dc.rightsAll rights reserved
dc.rightsAll Rights Reserveden
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/en
dc.subjectGeneral Relativity
dc.subjectNumerical Relativity
dc.subjectBlack Holes
dc.subjectHigher Dimensions
dc.titleNumerical Relativity in Higher Dimensional Spacetimes
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.publisher.departmentApplied Mathematics and Theoretical Physics
dc.date.updated2018-07-02T09:04:48Z
dc.identifier.doi10.17863/CAM.25057
dc.publisher.collegeTrinity Hall
dc.type.qualificationtitlePh.D. in Applied Mathematics and Theoretical Physics
cam.supervisorSperhake, Ulrich
cam.thesis.fundingtrue
rioxxterms.freetoread.startdate2018-07-02


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