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

Abstract

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...

Cosmic censorship and the evolution of d -dimensional charged evaporating black holes

“…For example, some of the earliest examples of naked singularity formation involves pinching-off of black strings (Gregory-Laflamme instability [5][6][7][8]) which takes place in higher dimensions. More recently, it was discovered that there may be topology-changing transitions for Reissner-Nordström de Sitter black holes and Gauss-Bonnet de Sitter black boles in higher dimensions that hint at violation of the weak cosmic censorship [9]. In addition, it was recently discovered that collisions of black holes can violate cosmic censorships in higher dimensions as energy that gets dissipated in gravitational waves decreases when dimensionality increases [10].…”

Black rings in large D membrane paradigm at the first order

“…See[12] for a short but excellent review 2. See[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], and[50][51][52] for other collaborations that use large D techniques similar to the framework of EST to study interesting and diverse problems.…”

Black Rings in Large $D$ Membrane Paradigm at the First Order

“…See[12] for a short but excellent review.2 See[35][36][37][38][39][40][41][42][43],[44][45][46][47][48][49], and[50][51][52] for other collaborations that use large D techniques similar to the framework of EST to study interesting and diverse problems.…”