Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions

By Sayantani Bhattacharyya, R. Loganayagam, Ipsita Mandal, Shiraz Minwalla, Ankita Sharma. 2008

249 citations recorded by the source corpus.

We generalize recent work to construct a map from the conformal Navier Stokes equations with holographically determined transport coefficients, in d spacetime dimensions, to the set of asymptotically locally AdSd+1 long wavelength solutions of Einstein's equations with a negative cosmological constant, for all 2$>d>2. We find simple explicit expressions for the stress tensor (slightly generalizing the recent result by Haack and Yarom (arXiv:0806.4602)), the full dual bulk metric and an entropy current of this strongly coupled conformal fluid, to second order in the derivative expansion, for arbitrary 2$>d>2. We also rewrite the well known exact solutions for rotating black holes in AdSd+1 space in a manifestly fluid dynamical form, generalizing earlier work in d = 4. To second order in the derivative expansion, this metric agrees with our general construction of the metric dual to fluid flows.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3eefa12ce61ec6f94aa224b19c8b2a1e31b56ab3

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Citations in the corpus

The fluid/gravity correspondence: a new perspective on the membrane paradigm (2010, unknown): “As already indicated, one immediate set of generalizations involved relating a d-dimensional conformal fluid to asymptotically AdSd+1 black hole (see [49] for the interesting case of d = 3 and [48, 25] for general d).”
Flat holography and Carrollian fluids (2018, background): “Hence the holographic limit r → ∞ is lightlike, already at finite k, which is a well known feature of the derivative expansion, expressed by construction in Eddington–Finkelstein-like coordinates [3, 4, 6].”
Adiabatic hydrodynamics: the eightfold way to dissipation (2015, background): “Translating the results of [65] we have89”
Gravity and hydrodynamics: lectures on the fluid-gravity correspondence (2009, methodology): “Subsequently, this discussion was generalized to other dimensions in [67, 68, 69].”
A Holographic View on Physics out of Equilibrium (2010, methodology): “As a simple example, [150] (in d = 4) and [140] (for general d) consider the explicitly-known case of rotating AdS black hole (which is asymptotically global AdSd+1) which describes a rigid fluid flow on S d−1×R (see also [151]), confirming the general construction indicated above.”
From Navier-Stokes to Einstein (2011, background): “In particular, excitations of a black hole horizon dissipate very much like those of a fluid [3–5, 12, 13, 28, 33–35], and there has been recent discussion of a holographic duality relating black holes and fluids [1, 8–10, 12, 14–17, 19, 21, 23, 24].”
A theory of first order dissipative superfluid dynamics (2011, methodology): “Our demonstration uses the technology of the so called fluid gravity correspondence [24, 25, 26, 27, 28, 21, 22, 29] but allows for the implementation of this map in an abstract manner that does not require us to know the explicit form”
Universal hydrodynamics of non-conformal branes (2009, unknown): “14 87 v2 [ he p- th ] 1 7”
Conformal hydrodynamics in Minkowski and de Sitter spacetimes (2010, background): “An extension of the solution (86) which includes second order corrections and a non vanishing chemical potential can be found in [16, 17, 13, 18].”