Static Gauss-Bonnet Black Holes at Large $D$

Abstract

We study the static black holes in the large $D$ dimensions in the Gauss-Bonnet gravity with a cosmological constant, coupled to the Maxewell theory. After integrating the equation of motion with respect to the radial direction, we obtain the effective equations at large $D$ to describe the nonlinear dynamical deformations of the black holes. From the perturbation analysis on the effective equations, we get the analytic expressions of the frequencies for the quasinormal modes of charge and scalar-type perturbations. We show that for a positive Gauss-Bonnet term, the black hole could become unstable only if the cosmological constant is positive, otherwise the black hole is always stable. However, for a negative Gauss-Bonnet term, we find that the black hole could always be unstable. The instability of the black hole depends not only on the cosmological constant and the charge, but also significantly on the Gauss-Bonnet term. Moreover, at the onset of instability there is a non-trivial static zero-mode perturbation, which suggests the existence of a new non-spherically symmetric solution branch. We construct the non-spherical symmetric static solutions of the large $D$ effective equations explicitly.

27 pages, 34 figures. arXiv admin note: text overlap with arXiv:1607.04713

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• Eikonal instability of Gauss-Bonnet-(anti-)de Sitter black holes
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• Charged Black Rings at large D
• Black holes in presence of cosmological constant: Second order in 1/D
• Holographic Bjorken Flow at Large-D
• Einstein-Gauss-Bonnet Black Rings at Large $D$
• Large D gravity and charged membrane dynamics with nonzero cosmological constant
• Stationary Solutions from the Large D Membrane Paradigm
• Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large $D$
• Photon Emission Near Myers-Perry Black Holes in the Large Dimension Limit
• The large $D$ membrane paradigm for general four-derivative theory of gravity with a cosmological constant
• The Fate of Instability of de Sitter Black Holes at Large $D$
• Instability in charged Gauss-Bonnet-de Sitter black holes
• The entropic force between two horizons of charged Gauss-Bonnet Black hole in de Sitter Spacetime
• Rotating black holes at large $D$ in Einstein-Gauss-Bonnet theory
• Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit
• Stress Tensor for Large-$D$ membrane at subleading orders