Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-06-12
J.Math.Phys.50:082502,2009
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, latex. v2: minor clarifications in section 3. v3: assumption of non-toroidal horizon topology made explicit, improve
Scientific paper
10.1063/1.3190480
We consider the near-horizon geometries of extremal, rotating black hole solutions of the vacuum Einstein equations, including a negative cosmological constant, in four and five dimensions. We assume the existence of one rotational symmetry in 4d, two commuting rotational symmetries in 5d and in both cases non-toroidal horizon topology. In 4d we determine the most general near-horizon geometry of such a black hole, and prove it is the same as the near-horizon limit of the extremal Kerr-AdS(4) black hole. In 5d, without a cosmological constant, we determine all possible near-horizon geometries of such black holes. We prove that the only possibilities are one family with a topologically S^1 X S^2 horizon and two distinct families with topologically S^3 horizons. The S^1 X S^2 family contains the near-horizon limit of the boosted extremal Kerr string and the extremal vacuum black ring. The first topologically spherical case is identical to the near-horizon limit of two different black hole solutions: the extremal Myers-Perry black hole and the slowly rotating extremal Kaluza-Klein (KK) black hole. The second topologically spherical case contains the near-horizon limit of the fast rotating extremal KK black hole. Finally, in 5d with a negative cosmological constant, we reduce the problem to solving a sixth-order non-linear ODE of one function. This allows us to recover the near-horizon limit of the known, topologically S^3, extremal rotating AdS(5) black hole. Further, we construct an approximate solution corresponding to the near-horizon geometry of a small, extremal AdS(5) black ring.
Kunduri Hari K.
Lucietti James
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