Abstract
We prove that D ≥ 5 dimensional stationary, non-static near-horizon geometries with (D−3) commuting rotational symmetries subject to the vacuum Einstein equations including a cosmological constant cannot have toroidal horizon topology. In D = 4 dimensions, the same result is obtained under the assumption of a non-negative cosmological constant.
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David, J.R., Mandal, G., Wadia, S.R.: Microscopic formulation of black holes in string theory. Phys. Rep. 369, 549–686 (2002). http://arxiv.org/abs/hep-th/0203048
Gauntlett, J.P., Gutowski, J.B., Hull, C.M., Pakis, S., Reall, H.S.: All supersymmetric solutions of minimal supergravity in five dimensions. Class. Quant. Grav. 20, 4587–4634 (2003). http://arxiv.org/abs/hep-th/0209114
Guica, M., Hartman, T., Song, W., Strominger, A.: The kerr/cft correspondence. Phys. Rev. D80, 124008 (2009). http://arxiv.org/abs/0809.4266
Hartman, T., Murata, K., Nishioka, T., Strominger, A.: Cft duals for extreme black holes. JHEP 04, 019 (2009). http://arxiv.org/abs/0902.1001
Compere, G., Murata, K., Nishioka, T.: Central charges in extreme black hole/cft correspondence. JHEP 05, 077 (2009). http://arxiv.org/abs/hep-th/0211290
Reall, H.S.: Higher dimensional black holes and supersymmetry. Phys. Rev. D68, 024024 (2003). http://arxiv.org/abs/0705.4214
Kunduri, H.K., Lucietti, J., Reall, H.S.: Near-horizon symmetries of extremal black holes. Class. Quant. Grav. 24, 4169–4190 (2007). http://arxiv.org/abs/0806.2051
Kunduri, H.K., Lucietti, J.: A classification of near-horizon geometries of extremal vacuum black holes. J. Math. Phys. 50, 082502 (2009). http://arxiv.org/abs/0909.3462
Hollands, S., Ishibashi, A.: All vacuum near horizon geometries in arbitrary dimensions. Annales Henri Poincaré 10, 1537–1557 (2010). http://arxiv.org/abs/0909.3462
Kim S., McGavran D., Pak J.: Torus group actions on simply connected mani-folds. Pac. J. Math. 53(2), 435–444 (1974)
Hollands, S., Yazadjiev, S.: A uniqueness theorem for stationary Kaluza–Klein black holes. Commun. Math. Phys. 302, 631–674. doi:10.1007/s00220-010-1176-7 (arXiv:0812.3036 [gr-qc])
Friedman, J.L., Schleich, K., Witt, D.M.: Topological censorship. Phys. Rev. Lett. 71, 1486–1489 (1993). http://arxiv.org/abs/gr-qc/9305017
Chruściel, P.T., Galloway, G.J., Solis, D.: Topological censorship for Kaluza–Klein space-times. Annales Henri Poincaré 10, 893–912 (2009). http://arxiv.org/abs/0808.3233
Galloway, G., Schleich, K., Witt, D., Woolgar, E.: The ads/cft correspondence conjecture and topological censorship. Phys.Lett. B 505, 255–262 (2001). http://arxiv.org/abs/hep-th/9912119
Moncrief V., Isenberg J.: Symmetries of cosmological cauchy horizons. Commun. Math. Phys. 89(3), 387–413 (1983)
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Communicated by Piotr T. Chrusciel.
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Holland, J. Non-Existence of Toroidal Cohomogeneity-1 Near-Horizon Geometries. Ann. Henri Poincaré 15, 407–414 (2014). https://doi.org/10.1007/s00023-013-0244-x
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DOI: https://doi.org/10.1007/s00023-013-0244-x