The large D black hole dynamics in AdS/dS backgrounds

Abstract

We have constructed a class of perturbative dynamical black hole solutions in presence of cosmological constant. We have done our calculation in large number of dimensions. The inverse power of dimension has been used as the perturbation parameter and our calculation is valid upto the first subleading order. The solutions are in one to one correspondence with a dynamical membrane and a velocity field embedded in the asymptotic geometry. Our method is manifestly covariant with respect to the asymptotic geometry. One single calculation and the same universal result works for both dS and AdS geometry or in case of AdS for both global AdS and Poincare patch. We have checked our final answer with various known exact solutions and the known spectrum of Quasi Normal modes in AdS/dS.

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

“…Note that in the β → 0 limit the subleading correction is zero which is consistent with the fact that in two derivative gravity the first subleading corrections to the metric are zero with the choice of auxiliary conditions used here [16]. 5 The results at second order in 1/D In [15] the algorithm to systematically correct the metric upto arbitrary orders in 1/D was presented for Einstein-Hilbert gravity.…”

“…Since, we want to study dynamical processes involving black holes, we promote ψ and u to be functions of the spacetime points with the following restrictions The ansatz metric solves for the EGB equation to leading order in large D [15,16,20] provided…”

“…We describe in brief the mechanism for this below. For the details of the procedure, one can look at the previous papers on the large D membrane paradigm [15][16][17] 11 .…”

“…In one the effective equations are obtained in terms of a dual object defined by its effective mass and momentum [8][9][10][11] 1 . The other formulation (which is the primary focus of this paper), recasts the black hole dynamics in terms of dynamics of a co-dimension one membrane propagating in the asymptotic spacetime of the black hole [13][14][15][16][17][18]. The membrane is characterised by its local shape and a worldvolume velocity field.…”

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

“…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 studies of the RN-dS and GB-dS black holes were initiated in [21] and [22].…”