The large dimension limit of a small black hole instability in anti-de Sitter space

Section: The Small Black Hole In Ads and Phase Separation On The Spherementioning

confidence: 99%

Submatrix deconfinement and small black holes in AdS

Berenstein

2018

“…The initial development of the subject is found in [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. More works related to large D are in [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. New dynamical black hole / brane metrics have been constructed for both asymptotically flat and dS/ AdS backgrounds [8-10, 12, 14, 20, 30, 35, 37].…”

Section: Contentsmentioning

confidence: 99%

Large D gravity and charged membrane dynamics with nonzero cosmological constant

Kundu

Nandi

2018

In this paper, we have found a class of dynamical charged 'black-hole' solutions to Einstein-Maxwell system with a non-zero cosmological constant in a large number of spacetime dimensions. We have solved up to the first sub-leading order using large D scheme where the inverse of the number of dimensions serves as the perturbation parameter. The system is dual to a dynamical membrane with a charge and a velocity field, living on it. The dual membrane has to be embedded in a background geometry that itself, satisfies the pure gravity equation in presence of a cosmological constant. Pure AdS / dS are particular examples of such background. We have also obtained the membrane equations governing the dynamics of charged membrane. The consistency of our membrane equations is checked by calculating the quasi-normal modes with different Einstein-Maxwell System in AdS/dS. arXiv:1806.08515v3 [hep-th] 13 Dec 2018Firstly, they generate a new class of dynamical black hole solutions of Einstein equations which are very difficult to solve otherwise (even numerically). Secondly, through these constructions, we could see a duality between the dynamical horizons of the black hole/brane metric and a co-dimension one dynamical membrane, embedded in the asymptotic background geometry. This membrane-gravity duality allows us to analyse the complicated dynamics of the black holes from a different angle, which might turn out to be useful in future for some realistic calculation.In this paper, our goal is to extend the 'background covariant' technique of [35] to Einstein-Maxwell system in presence of cosmological constant. For this case, the dual system would be a codimension-one dynamical charged membrane, embedded in the asymptotic dS / AdS metric. The motivation for our work is two-fold. The first is, of course, to see how the whole technique of background-covariantization works for Einstein-Maxwell system, which, in terms of complexity, is just at the next level, compared to the pure gravity system. Indeed we have noticed that unlike the uncharged case, only naive covariantization of the flat spaceequations of the charged membrane (as derived in [9]) will not give the correct duality and we need to add a term proportional to the background curvature even at the first subleading order in O 1 D expansion. This is indeed one of the interesting observations in our paper. The second piece of motivation is as follows. We know that in asymptotically AdS geometry there exist another set of perturbative solutions to Einstein-Maxwell system. These are black holes/branes constructed in a derivative expansion and are dual to dynamical charged fluid living at the boundary of AdS. Recent works can be found in [18,34,38]. At this point, it is natural to ask whether there exists any overlap regime for these two types of perturbations, and if so, whether the two metrics agree. In the best possible scenario, the outcome of this comparison could be a duality between the dynamics of a charged fluid and charged membrane in a large number of dimensions, wh...

“…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.…”

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confidence: 99%

Black rings in large D membrane paradigm at the first order

Mandlik

2021

Black rings are the black objects found in D spacetime dimensional gravity when D ≥ 5. These have event horizon topology SD−3× S1. In this work the solutions of the large D membrane paradigm dual to stationary black rings in Einstein-Maxwell theory with or without cosmological constant are studied. It is shown that the first order membrane equations can only admit static asymptotically flat black rings, and the equilibrium angular velocity for the asymptotically AdS black rings at large D was obtained. The thermodynamic and dynamic stability of the asymptotically flat black ring solutions is studied. The apparent shortcomings of some of these results are argued to be curable within the large D membrane paradigm framework.