CFT dual of charged AdS black hole in the large dimension limit

Guo, Er-dong; Li, Miao; Sun, Jwo‐Shiun

doi:10.1142/s0218271816500851

Cited by 12 publications

(7 citation statements)

References 49 publications

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“…However, n may need to be very large for the 1/n expansion to be reliable there. 13 With our normalization (3.1) for the gauge field, µ is twice the one in [33].…”

Section: Polarized Branesmentioning

confidence: 99%

Hydro-elastic complementarity in black branes at large D

Emparan

Izumi

Luna

et al. 2016

J. High Energ. Phys.

143

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We obtain the effective theory for the non-linear dynamics of black branesboth neutral and charged, in asymptotically flat or Anti-deSitter spacetimes -to leading order in the inverse-dimensional expansion. We find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. The two views are complementary: the same variable is regarded in one case as the energy density of the fluid, in the other as the deformation of the elastic membrane. The large-D theory captures finite-wavelength phenomena beyond the conventional reach of hydrodynamics. For asymptotically flat charged black branes (either Reissner-Nordstrom or p-brane-charged black branes) it yields the non-linear evolution of the Gregory-Laflamme instability at large D and its endpoint at stable non-uniform black branes. For Reissner-Nordstrom AdS black branes we find that sound perturbations do not propagate (have purely imaginary frequency) when their wavelength is below a certain charge-dependent value. We also study the polarization of black branes induced by an external electric field.

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“…However, n may need to be very large for the 1/n expansion to be reliable there. 13 With our normalization (3.1) for the gauge field, µ is twice the one in [33].…”

Section: Polarized Branesmentioning

confidence: 99%

Hydro-elastic complementarity in black branes at large D

Emparan

Izumi

Luna

et al. 2016

J. High Energ. Phys.

143

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“…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

J. High Energ. Phys.

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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...

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“…By considering the addition of charge and possibly dilatonic scalar fields to the black hole one obtains different universality classes of near-horizon geometries (Emparan et al, 2013b) (see also (Guo et al, 2016)). These geometries can all be regarded as solutions of theories where matter is added to (2.16).…”

Section: B Universalitymentioning

confidence: 99%

The Large D Limit of Einstein's Equations

Emparan,

Herzog

2020

Preprint

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I General aspects I. Large N and large D expansions A. The nature of the large D limit B. Organization of this review Outline II. The large D geometry of stationary black holes A. Near and far zones B. Universality C. Strings near the horizon? III. Decoupled and non-decoupled dynamics of large D black holes A. Quasinormal spectrum B. Qualitative features from the radial potential C. Non-decoupled modes D. Decoupled modes E. Cosmological constant and rotation F. Asymptotic non-convergence of the expansion IV. Effective theories of black holes at large D A. Aspects of effective theories of black hole dynamics B. Hydro Review C. Large D vs. AdS/CFT decoupling and Fluid/Gravity D. The large D effective membrane theory 1. The membrane equations 2. Playing with soap bubbles 3. Fluid stress-energy, entropy, action, and coupling to radiation 4. Extensions 5. Limitations 6. Membrane paradigms E. Effective theory for black branes 1. Black brane equations 2. Extensions 3. Black holes as blobs on a brane II Applications V. The Gregory-Laflamme instability at large D Further Extensions VI. Black hole collisions and mergers A. General aspects B. Cosmic censorsip violation in black hole collisions VII. Holographic applications A. Holographic Hydrodynamics B. AdS/CMT Breaking Translation Symmetry Holographic Superconductor C. AdS/QCD Bjorken Flow Small Black Holes III Other directions VIII. Quantum black holes, quantum gravity and strings A. Large D limit of Hawking radiation B. Large D matrix models C. Large D entanglement D. Large D strings IX. Higher-derivative gravity X. Beyond decoupling A. Non-decoupled waves and hair B. Short-scale structure, singularities, and topology change C. Critical collapse and Choptuik scaling XI. Gravitational radiation A. Shockwave collisions B. An effective theory of gravitational waves?24 This is the uniform black brane case of (4.47) and (4.49) with constant m = r n 0 and p i = 0 (and ρ → r, σ i /

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CFT dual of charged AdS black hole in the large dimension limit

Cited by 12 publications

References 49 publications

Hydro-elastic complementarity in black branes at large D

Hydro-elastic complementarity in black branes at large D

Large D gravity and charged membrane dynamics with nonzero cosmological constant

The Large D Limit of Einstein's Equations

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