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dc.contributor.advisorLucietti, James
dc.contributor.advisorSoler, Joan Simon
dc.contributor.authorLi, Ka Ki
dc.contributor.authorLi, Carmen
dc.date.accessioned2016-06-09T10:19:58Z
dc.date.available2016-06-09T10:19:58Z
dc.date.issued2016-06-29
dc.identifier.urihttp://hdl.handle.net/1842/15856
dc.description.abstractIn this thesis we study near-horizon geometries of extreme black holes. We first consider stationary extreme black hole solutions to the Einstein-Yang-Mills theory with a compact semi-simple gauge group in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon AdS2 symmetry and deduce its near-horizon geometry must be that of the abelian embedded extreme Kerr-Newman (AdS) black hole. We show that the near-horizon geometry of any static black hole is a direct product of AdS2 and a constant curvature space. We then consider near-horizon geometry in Einstein gravity coupled to a Maxwell field and a massive complex scalar field, with a cosmological constant. We prove that assuming non-zero coupling between the Maxwell and the scalar fields, there exists no solution with a compact horizon in any dimensions where the massive scalar is non-trivial. This result generalises to any scalar potential which is a monotonically increasing function of the modulus of the complex scalar. Next we determine the most general three-dimensional vacuum spacetime with a negative cosmological constant containing a non-singular Killing horizon. We show that the general solution with a spatially compact horizon possesses a second commuting Killing field and deduce that it must be related to the BTZ black hole (or its near-horizon geometry) by a diffeomorphism. We show there is a general class of asymptotically AdS3 extreme black holes with arbitrary charges with respect to one of the asymptotic-symmetry Virasoro algebras and vanishing charges with respect to the other. We interpret these as descendants of the extreme BTZ black hole. However descendants of the non-extreme BTZ black hole are absent from our general solution with a non-degenerate horizon. We then show that the first order deformation along transverse null geodesics about any near-horizon geometry with compact cross-sections always admits a finite-parameter family of solutions as the most general solution. As an application, we consider the first order expansion from the near-horizon geometry of the extreme Kerr black hole. We uncover a local uniqueness theorem by demonstrating that the only possible black hole solutions which admit a U(1) symmetry are gauge equivalent to the first order expansion of the extreme Kerr solution itself. We then investigate the first order expansion from the near-horizon geometry of the extreme self-dual Myers-Perry black hole in 5D. The only solutions which inherit the enhanced SU(2) X U(1) symmetry and are compatible with black holes correspond to the first order expansion of the extreme self-dual Myers-Perry black hole itself and the extreme J = 0 Kaluza-Klein black hole. These are the only known black holes to possess this near-horizon geometry. If only U(1) X U(1) symmetry is assumed in first order, we find that the most general solution is a three-parameter family which is more general than the two known black hole solutions. This hints the possibility of the existence of new black holes.en
dc.contributor.sponsorotheren
dc.language.isoenen
dc.publisherThe University of Edinburghen
dc.relation.hasversionCarmen Li and James Lucietti. Uniqueness of extreme horizons in Einstein-Yang- Mills theory. Class.Quant.Grav., 30:095017, 2013.en
dc.relation.hasversionCarmen Li and James Lucietti. Transverse deformations of extreme horizons. 2015.en
dc.relation.hasversionCarmen Li and James Lucietti. Three-dimensional black holes and descendants. Phys.Lett., B738:48-4, 2014.en
dc.subjectBlack holeen
dc.subjectgeneral relativityen
dc.subjectdifferential geometryen
dc.titleExtreme Black Holes and Near-Horizon Geometriesen
dc.typeThesis or Dissertationen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD Doctor of Philosophyen


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