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 nonspherically symmetric solution branch. We construct the non-spherical symmetric static solutions of the large D effective equations explicitly.

Charged black rings at large D

“…The shape of the membrane that is the topology of the horizon is described by the embedding of the membrane into a background spacetime, and the non-linear dynamics of the membrane is determined by the effective equations obtained by integrating out the radial direction of the Einstein equations. By solving the effective equations with proper embeddings of the membrane, one can construct different black hole solutions and furthermore study their dynamics perturbatively to find the quasinormal modes or determine numerically the end points of their evolutions under the unstable perturbations [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. From a broader perspective, the large D effective theory of the black hole is similar to the effective theories in the fluid/gravity correspondence [25] and the blackfold approach [26,27].…”

Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling

“…• Gravitational perturbations of Einstein-Gauss-Bonnet-AdS spherical black holes (shown here and in [16,57]). …”

Photon emission near Myers-Perry black holes in the large dimension limit

“…which is related to ξ 1 by ξ 2 1 − 1 = ξ 2 4 . The other case is 0 < ξ 3 < 1, in this case the constraint on (q, λ) becomes 29) and the identify 1 − ξ 2 1 = ξ 2 4 follows immediately. In this case, the analytical result of the radial integral in the far region takes the form…”

“…The class of light modes decouples from the asymptotic region such that one can formulate an effective theory of black hole [27,28]. The effective theory has been widely applied to study of various issues on black hole, and has also been developed for the black holes in the Gauss-Bonnet gravity [29].…”