On Black Hole Stability in Critical Gravities

Abstract

We consider extended cosmological gravities with Ricci tensor and scalar squared terms in diverse dimensions. These theories admit solutions of Einstein metrics, including the Schwarzschild-Tangherlini AdS black holes, whose mass and entropy vanish at the critical point. We perform linearized analysis around the black holes and show that in general the spectrum consists of the usual spin-2 massless and ghost massive modes. We demonstrate that there is no exponentially-growing tachyon mode in the black holes. At the critical point, the massless spin-2 modes have zero energy whilst the massive spin-2 modes are replaced by the log modes. There always exist certain linear combination of massless and log modes that has negative energy. Thus the stability of the black holes requires that the log modes to be truncated out by the boundary condition.

16 pages, minor corrections, further comments and references added

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• Linearized Modes in Extended and Critical Gravities
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• Critical gravity as van Dam-Veltman-Zakharov discontinuity in anti de Sitter space
• Supersymmetric Asymptotic AdS and Lifshitz Solutions in Einstein-Weyl and Conformal Supergravities
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• Exact Solutions of General Relativity and Quadratic Gravity in Arbitrary Dimension
• Supersymmetry of the Schrodinger and PP Wave Solutions in Einstein-Weyl Supergravities
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• Hawking Radiation and Tunneling Mechanism for a New Class of Black Holes in Einstein-Gauss-Bonnet Gravity
• Critical gravity with a scalar field in four dimensions
• Causality Constraint on Noncritical Einstein-Weyl Gravity