## Extreme Black Holes and Near-Horizon Geometries

dc.contributor.advisor | Lucietti, James | |

dc.contributor.advisor | Soler, Joan Simon | |

dc.contributor.author | Li, Ka Ki | |

dc.contributor.author | Li, Carmen | |

dc.date.accessioned | 2016-06-09T10:19:58Z | |

dc.date.available | 2016-06-09T10:19:58Z | |

dc.date.issued | 2016-06-29 | |

dc.identifier.uri | http://hdl.handle.net/1842/15856 | |

dc.description.abstract | In 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.sponsor | other | en |

dc.language.iso | en | en |

dc.publisher | The University of Edinburgh | en |

dc.relation.hasversion | Carmen Li and James Lucietti. Uniqueness of extreme horizons in Einstein-Yang- Mills theory. Class.Quant.Grav., 30:095017, 2013. | en |

dc.relation.hasversion | Carmen Li and James Lucietti. Transverse deformations of extreme horizons. 2015. | en |

dc.relation.hasversion | Carmen Li and James Lucietti. Three-dimensional black holes and descendants. Phys.Lett., B738:48-4, 2014. | en |

dc.subject | Black hole | en |

dc.subject | general relativity | en |

dc.subject | differential geometry | en |

dc.title | Extreme Black Holes and Near-Horizon Geometries | en |

dc.type | Thesis or Dissertation | en |

dc.type.qualificationlevel | Doctoral | en |

dc.type.qualificationname | PhD Doctor of Philosophy | en |