Large rotating AdS black holes from fluid mechanics

By Sayantani Bhattacharyya, Subhaneil Lahiri, R. Loganayagam, Shiraz Minwalla. 2007

183 citations recorded by the source corpus.

We use the AdS/CFT correspondence to argue that large rotating black holes in global AdSD spaces are dual to stationary solutions of the relativistic Navier-Stokes equations on SD−2. Reading off the equation of state of this fluid from the thermodynamics of non-rotating black holes, we proceed to construct the nonlinear spinning solutions of fluid mechanics that are dual to rotating black holes. In all known examples, the thermodynamics and the local stress tensor of our solutions are in precise agreement with the thermodynamics and boundary stress tensor of the spinning black holes. Our fluid dynamical description applies to large non-extremal black holes as well as a class of large non-supersymmetric extremal black holes, but is never valid for supersymmetric black holes. Our results yield predictions for the thermodynamics of all large black holes in all theories of gravity on AdS spaces, for example, string theory on AdS5 × S5 and M theory on AdS4 × S7 and AdS7 × S4.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2d6d49eaaa9c7fd37cf917ad38c314659e4fc779

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Citations in the corpus

Gravity and hydrodynamics: lectures on the fluid-gravity correspondence (2009, background): “To discuss hydrodynamics we need to be in the long-wavelength regime which is achieved only in the deconfined phase at high temperatures [65].”
Hydrodynamics from charged black branes (2008, background): “The presence of such an effect was indirectly observed by the authors of [42] where they noted a discrepancy between the thermodynamics of charged rotating AdS blackholes and the fluid dynamical prediction with the third term in the charge current absent.”
A theory of first order dissipative superfluid dynamics (2011, result): “In such a limit, we recover the results of [21, 22, 20] (see also [23]).”
Parity-violating hydrodynamics in 2 + 1 dimensions (2011, background): “One example is given by a fluid on a sphere [59] where Ω = 2ω cos θ/(1 − ω2 sin(2) θ), and θ is the polar angle on the two-sphere.”
Fluid dynamics of R-charged black holes (2008, background): “In [40] it was shown that in this limit, even though the temperature vanishes, the mean free path is not necessarily vanishing and one might expect a hydrodynamic description of the theory in this regime.”
Relativistic viscous hydrodynamics, conformal invariance, and holography (2007, unknown): “2.3 Conformal invariance in first-order hydrodynamics It is straightforward to check that if T �ν transforms as in Eq. (2.12) and T � � = 0, then its covariant divergence transforms homogeneously: ∇� T �ν → e (d+2)ω ∇� T �ν , hence the hydrodynamic equation ∇� T �ν = 0 is Weyl invariant [ 15 ].”
Holographic Hydrodynamics with a Chemical Potential (2009, background): “However, the two derivative coupling κ is known to play a role when rotation is introduced [52].”
Black holes as effective geometries (2008, background): “In an interesting recent work, a connection between non-supersymmetric black holes and interacting fluid dynamics was found [76, 77], which suggests that the type of dual descriptions in terms of free gases of particles that we used in the supersymmetric cases may not be sufficient.”
Black Holes in Higher Dimensions (2008, methodology): “For sufficiently large black holes, one can study the dual CFT using a fluid mechanics approximation, which gives quantitative agreement with black-hole thermodynamics [14].”
Constraints on fluid dynamics from equilibrium partition functions (2012, background): “3) (1)Equilibrium Partition functions special curved manifolds or with particular background gauge fields have been studied before in [16, 17, 18]”
Weak Field Black Hole Formation in Asymptotically AdS Spacetimes (2009, background): “See also [24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34] for related line of development.”
Thermodynamics and instabilities of a strongly coupled anisotropic plasma (2011, background): “At a more theoretical level, motivation for our work is provided by the fluid/gravity correspondence [58, 59, 60, 61, 62, 63, 64, 65] (see [66, 67, 68] for reviews), which asserts that the long-wavelength effective dynamics of black brane horizons in asymptotically anti-de Sitter spacetimes is equiv”
Comments on string theory backgrounds with non-relativistic conformal symmetry (2008, background): “The boundary stress-energy tensor in this coordinate system is calculated in [30].”
Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions (2008, background): “3.1 Equations of motion and uniform brane solutions 10 3.2 Slow variation and bulk tubes and our zero order ansatz 11 3.3 Perturbation theory at long wavelengths 14 3.4 Weyl Covariance 15”
Black rings in (Anti)-de Sitter space (2008, background): “However, a thorough analysis of the relativistic Navier-Stokes equation for a rotating fluid on the boundary geometry R × S has not revealed other solutions than the duals of rotating AdS black holes [9] (see also [10]).”