Perturbations and Stability of Static Black Holes in Higher Dimensions(Chapter 6,Higher Dimensional Black Holes)
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概要
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In this chapter we consider perturbations and stability of higher dimensional black holes focusing on the static background case. We first review a gauge-invariant formalism for linear perturbations in a fairly generic class of (m+n)-dimensional spacetimes with a warped prodnct metric, including black hole geometry. We classify perturbations of such a background into three types, the tensor, vector and scalar-type, according to their tensorial behavior on the n-dimensional part of the background spacetime, and for each type of perturbations, we introduce a set of manifestly gauge invariant variables. We then introduce harmonic tensors and write down the equations of motion for the expansion coefficients of the gauge invariant perturbation variables in terms of the harmonics. In particular, for the tensor-type perturbations a single master equation is obtained in the (m+n)-dimensional background, which is applicable for perturbation analysis of not only static black holes but also some class of rotating black holes as well as black-branes. For the vector and scalar type, we derive a set of decoupled master equations when the background is a (2+n)-dimensional static black hole in the Einstein-Maxwell theory with a cosmological constant. As an application of the master equations. we review the stability analysis of higher dimensional charged static black holes with a cosmological constant. We also briefly review the recent results of a generalization of the perturbation formulae presented here and stability analysis to static black holes in generic Lovelock theory.
- 2011-08-29
著者
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小玉 英雄
Kek Tsukuba Jpn
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KODAMA Hideo
Department of Physics, College of Liberal Arts and Sciences Kyoto University
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KODAMA Hideo
IPNS, KEK and the Graduate University of Advanced Studies
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Ishibashi Akihiro
Theory Center Ipns Kek:department Of Physics Kinki University
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Ishibashi Akihiro
Theory Center Institute Of Particle And Nuclear Studies High Energy Accelerator Research Organizatio
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KODAMA Hideo
Theory Center, IPNS, KEK
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Kodama Hideo
Theory Center Ipns Kek:the Graduate University Of Advanced Studies
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Kodama Hideo
Theory Center Institute Of Particle And Nuclear Studies Kek:department Of Particles And Nuclear Phys
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KODAMA Hideo
Department of Physics, Osaka University : Department of Physics, Kyoto University
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KODAMA Hideo
Theory Center, Institute of Particles and Nuclear Studies, KEK
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KODAMA Hideo
Yakawa Institute for Theoretical Physics, Kyoto University
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KODAMA Hideo
Theory Center, Institute of Particle and Nuclear Studies, KEK:Department of Particles and Nuclear Physics, The Graduate University for Advanced Studies
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KODAMA Hideo
Department of Particle and Nuclear Physics, Graduate University for Advanced Studies:Theory Center, KEK
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ISHIBASHI Akihiro
Theory Division, Institute of Particle and Nuclear Studies
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