Charged black rings at large D

Self Cite

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.

Section: Jhep05(2017)025mentioning

confidence: 74%

Static Gauss-Bonnet black holes at large D

Chen¹,

Li²

2017

Self Cite

“…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...

“…It has been known that up to the linear order of the rotation parameter a the higher dimensional slowly rotating black holes in the EGB theory are easy to construct, since in this case a only appears in the component g vΦ which can be treated as a perturbation [48]. Now we are considering the slowly rotating black holes in the EGB theory with a small a = O(1/ √ n), the form of the metric should be the same as that in the Einstein gravity [33]. Note that in the above metric ansatz the information of the horizon shape is undetermined, so that we can discuss various stationary solutions including the black ring, black hole and the (boosted) black string from the same ansatz.…”

Section: Finkelsteins Coordinatesmentioning

confidence: 99%

“…The membrane is described by the way it is embedded in the background and its dynamics is governed by the effective equations obtained from the 1/D expansion of the Einstein equations. Solving the effective equations with different embeddings, one can construct the black hole solutions with various topologies, and furthermore to study their dynamics [23][24][25][26][27][28][29][30][31][32][33][34][35]. For example, in [25] by solving the effective equations of slowing rotating black holes with the embedding into a flat background in the ring coordinates, the black ring solution was constructed analytically in the 1/D expansion.…”

Section: Introductionmentioning

confidence: 99%

Einstein-Gauss-Bonnet black rings at large D

Chen

Zhang

2018

Self Cite

We study the black ring solution in the Einstein-Gauss-Bonnet (EGB) theory at large D. By using the 1/D expansion in the near horizon region we derive the effective equations for the slowly rotating black holes in the EGB theory. The effective equations describe the nonlinear dynamics of various stationary solutions, including the EGB black ring, the slowly rotating EGB black hole and the slowly boosted EGB black string. By different embeddings we construct these stationary solutions explicitly. By performing the perturbation analysis of the effective equations, we obtain the quasinormal modes of the EGB black ring. We find that thin EGB black ring becomes unstable against non-axisymmetric perturbation. Furthermore, we numerically evolve the effective equations in a particular case to study the final state of the instability, and find that the thin black ring becomes the stable non-uniform black ring at late time, which gives a relative strong evidence to support the conjecture given in [25]. *