Stability of Topological Black Holes

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dc.creatorBirmingham, Danny
dc.creatorMokhtari, Susan
dc.date2007-09-14
dc.date2007-11-28
dc.date.accessioned2026-07-07T11:19:21Z
dc.date.available2026-07-07T11:19:21Z
dc.descriptionWe explore the classical stability of topological black holes in d-dimensional anti-de Sitter spacetime, where the horizon is an Einstein manifold of negative curvature. According to the gauge invariant formalism of Ishibashi and Kodama, gravitational perturbations are classified as being of scalar, vector, or tensor type, depending on their transformation properties with respect to the horizon manifold. For the massless black hole, we show that the perturbation equations for all modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of potential gravitational instabilities. We establish a necessary and sufficient condition for stability, in terms of the eigenvalues $λ$ of the Lichnerowicz operator on the horizon manifold, namely $λ\geq -4(d-2)$. For the case of negative mass black holes, we show that a sufficient condition for stability is given by $λ\geq -2(d-3)$.
dc.description20 pages, Latex, v2 refined analysis of boundary conditions in dimensions 4,5,6, additional references
dc.identifierhttps://arxiv.org/abs/0709.2388
dc.identifierhttp://arxiv.org/abs/0709.2388
dc.identifierPhys.Rev.D76:124039,2007
dc.identifierdoi:10.1103/PhysRevD.76.124039
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/193654
dc.subjectHigh Energy Physics - Theory
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleStability of Topological Black Holes
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