Einstein-Gauss-Bonnet black strings at large D

We find the equations of motion of membranes dual to the black holes in Einstein-Gauss-Bonnet (EGB) gravity to leading order in 1/D in the large D regime. We also find the metric solutions to the EGB equations to first subleading order in 1/D in terms of membrane variables. We propose a world volume stress tensor for the membrane whose conservation equations are equivalent to the leading order membrane equations. We work out the light quasi-normal mode spectrum of static black holes in EGB gravity from the linearised fluctuations of static, round membranes. Also, the effective equations for stationary black holes and the spectrum of linearised spectrum about black string configurations has been obtained using the membrane equation for EGB gravity. All our results are worked out to linear order in the Gauss-Bonnet parameter.

Section: Stationary Solutionssupporting

confidence: 78%

Section: Introductionmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 79%

See 1 more Smart Citation

The large D membrane paradigm for Einstein-Gauss-Bonnet gravity

Saha

2019

“…where, β is an O(D 0 ) quantity 5 .The leading order in 1/D effective equation for EGB gravity non-perturbatively in the Gauss-Bonnet parameter in the mass momentum formalism were worked out in [22]. In this paper we work out the membrane equations to subleading order in 1/D upto linear order in β.…”

Section: Introductionmentioning

confidence: 99%

Large D membrane for higher derivative gravity and black hole second law

Dandekar

Saha

2020

We derive the effective equations of the membranes dual to black holes in a particular theory of higher derivative gravity namely Einstein-Gauss-Bonnet (EGB) gravity at sub-leading order in 1/D upto linear order in the Gauss-Bonnet (GB) parameter β. We find an expression for an entropy current which satisfies a local version of second law onshell in this regime. We also derive the membrane equations upto leading order in 1/D but non-perturbatively in β for EGB gravity. In this regime we write down an expression for a world-volume stress tensor of the membrane and also work out the effective membrane equation for stationary black holes.

“…This is reminiscent of the fact that in the ringdown phase of the coalescence of a binary black holes, the modes with = 2 are dominant. 3 More large D studies on the GB black objects can be found in [30][31][32][33][34]. In panel (d) the mass density focuses on the equator, i.e.…”

Section: Gb-ds Black Holementioning

confidence: 99%

The fate of instability of de Sitter black holes at large D

Li¹,

Zhang²,

Chen³

2019

Self Cite

We study non-linearly the gravitational instabilities of the Reissner-Nordstrom-de Sitter and the Gauss-Bonnet-de Sitter black holes by using the large D expansion method. In both cases, the thresholds of the instability are found to be consistent with the linear analysis, and on the thresholds the evolutions of the black holes under the perturbations settle down to stationary lumpy solutions. However, the solutions in the unstable region are highly time-dependent, and resemble the fully localized black spots and black ring with S D−2 and S 1 × S D−3 topologies, respectively. Our study indicates the possible transition between the lumpy black holes and the localized black holes in higher dimensions. * One important aspect of a black hole is its stability under gravitational perturbations. In contrast to the D = 4 case, the black holes in higher dimensions can have various topologies and could be unstable under gravitational perturbations. This was first illustrated by Gregory and Laflamme (GL) for the black strings (branes) [1]. Since then, a lot of black objects with distinct topologies in higher dimensions have been discovered, and similar instabilities have been demonstrated [2-4]. Compared with the linear dynamics, determining the final state of the unstable black objects is more intriguing, as which may lead to violation of the Weak Cosmic Censorship and topology-changing transitions of black hole horizons. A well-known example is the non-linear evolution of the GL instability of the five dimensional black string [5]. Recently, a new type of dynamical instability was discovered for the higher dimensional Reissner-Nordstrom-de Sitter (RN-dS) and Gauss-Bonnet-de Sitter (GB-dS) black holes [6-8]. The RN-dS black hole becomes gravitationally unstable for large values of the electric charge and cosmological constant. The GB-dS black hole is unstable as well when the cosmological constant is sufficiently large. In both cases the instability is triggered by a positive cosmological constant.Such instability is called "Λ instability". One interesting feature of the "Λ instability" is that such instability only happens with an electromagnetic field or a GB term. Moreover, it was noticed that at the threshold point of the instability the shape of the RN-dS black hole is slightly deformed.This fact suggests that the unstable RN-dS black hole could either split into two black holes or transform into a black ring. However, due to the limitation of the linear analysis, the final stage of the evolution of the unstable black holes has not been settled yet, though some non-linear efforts have been made from the viewpoint of gravitational collapse [9].The goal of this work is to better understand the "Λ instability" of the two kinds of black holes by using the large D expansion method [10]. Taking the large dimension limit, the non-trivial dynamics of black holes is localized at the near region of the horizon, such that a full non-linear effective theory can be formulated [11][12][13][14][15][16][17][18][19][20]. The large D s...