Local Fluid Dynamical Entropy from Gravity

By Sayantani Bhattacharyya, V. Hubeny, R. Loganayagam, Gautam Mandal, Shiraz Minwalla, T. Morita, M. Rangamani, Harvey Reall. 2008

243 citations recorded by the source corpus.

Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and determine the location of the horizon order by order in a boundary derivative expansion. Intriguingly, the derivative expansion allows us to determine the location of the event horizon in the bulk as a local function of the fluid dynamical variables. We define a natural map from the boundary to the horizon using ingoing null geodesics. The area-form on spatial sections of the horizon can then be pulled back to the boundary to define a local entropy current for the dual field theory in the hydrodynamic limit. The area theorem of general relativity guarantees the positivity of the divergence of the entropy current thus constructed.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1d0d4382329deb89510286b8c1c1cb4fe732acaa

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Citations in the corpus

Gravity and hydrodynamics: lectures on the fluid-gravity correspondence (2009, methodology): “In [66] the global aspects of the bulk geometry were discussed and a geometric construction of the fluid entropy current was given.”
Fluid dynamics of R-charged black holes (2008, methodology): “ that is responsible for having Ω 6= 0. 5 leading to (13). One may construct all possible Weyl-covariant vectors composed of two derivatives which are orthogonal to the velocity ﬁeld. See for example [29, 30, 31, 32, 33, 19, 15] for a more elaborate discussion on the construction of Weyl invariant q”
Numerical methods for finding stationary gravitational solutions (2015, background): “These include the matched asymptotic expansion [37]; the non-interacting thermodynamical model and the higher order matched asymptotic expansion for nonlinear solutions [38–45]; the fluid/gravity correspondence (a long-wavelength gradient expansion) [46, 47] reviewed in [27, 48]; the blackfold appro”
A theory of first order dissipative superfluid dynamics (2011, methodology): “1 2 gmnVψ|Dψ| 2 + 1 2 Vψ((Dmψ)(Dnψ)∗ +(Dnψ)(Dmψ)∗) . (6.4) Our strategy for computing the parity odd corrections to the entropy current and the parity odd transport coeﬃcients closely follows that of [25, 27, 22, 23, 16, 10]. We ﬁrst construct a stationary solution to the equations of motion (6.3) i”
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”
The AdS/CFT correspondence (2014, background): “Moreover, by construction the solution remains regular well past the event horizon [130] (55).”
Adiabatic hydrodynamics: the eightfold way to dissipation (2015, background): “One can furthermore check that the pull-back of the Wald functional on the horizon onto the boundary, to define a boundary entropy current as in [64] will indeed give a contribution of the form (10.”
The holographic fluid dual to vacuum Einstein gravity (2011, background): “This can be worked out perturbatively in the non-relativistic expansion, as in the analogous computation in [22].”
Constraints on fluid dynamics from equilibrium partition functions (2012, background): “orrections to the equations of Einstein gravity? Within gravity can one prove directly that the existence of equilibrium implies the existence of a Wald entropy increase theorem (and so the existence [25] of a positive divergence entropy current)(see [26] for related discussion)? We feel that severa”
Relativistic viscous fluid dynamics and non-equilibrium entropy (2009, background): “): (πT)2 4πη A2 = − 1 8 , (πT)2 4πη A3 = 1 8 , (πT)2 4πη B1 = 1 4 . (5.2) These values precisely correspond to those for the entropy current derived from the horizon of a black hole in AdS5 (see Ref. [22]). This serves as another consistencycheck of the above approach. It would be interesting to cal”
Nonlinear fluid dynamics from gravity (2007, background): “This synopsis is based on the following three papers, [1], [2] and [3].”
A Holographic View on Physics out of Equilibrium (2010, background): “At first order, the position of the horizon is unchanged, whereas at second order it is corrected by terms which scale with square of the shear and vorticity (see [149], [24] for explicit expressions.”
Hydrodynamics from charged black branes (2008, background): “Further, it would be interesting to derive an entropy current for the charged fluid following the proposal outlined in [2].”
The fluid/gravity correspondence: a new perspective on the membrane paradigm (2010, unknown): “This can be solved algebraically, order by order in , and takes the schematic form [24]”