Wilsonian approach to fluid/gravity duality

By Irene Bredberg, Cynthia Keeler, V. Lysov, Andrew Strominger. 2010

210 citations recorded by the source corpus.

The problem of gravitational fluctuations confined inside a finite cutoff at radius r = rc outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff rc the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant D (rc) is derived. The dependence on rc is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for D(∞) reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant D(horizon) reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio $ \frac{\eta }{s} $ is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/e58059e37c466e3bf015219231f31c11a1a3b8de

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Citations in the corpus

Electron stars for holographic metallic criticality (2010, unknown): “This perspective suggests that in the bulk one should focus on the near horizon region of the geometry, as argued most explicitly in [59, 60].”
From Navier-Stokes to Einstein (2011, methodology): “In this section we will improve on the analysis of [28] by solving the shooting problem in the long wavelength -expansion without a simultaneous linearized expansion.”
TT deformations in general dimensions (2018, unknown): “Note that one can set up a Dirichlet problem at finite radius not just in asymptotically AdS geometries, but also in Ricci flat spacetimes [17–20].”
The holographic fluid dual to vacuum Einstein gravity (2011, background): “The expansion is therefore in general physically distinct from a near-horizon expansion, although it would certainly be useful to understand in more detail the limit in which rc is taken to be close to the horizon, following [7].”
Integrating out geometry: holographic Wilsonian RG and the membrane paradigm (2010, background): “1, one can push the cut-off surface into some relevant infrared (IR) region of the bulk geometry and then forget the rest of the spacetime (see also [24, 25] for recent works emphasizing similar ideas).”
Holographic and Wilsonian renormalization groups (2010, background): “[37, 38] also takes a Wilsonian approach to transport calculations, and Refs.”
A Holographic View on Physics out of Equilibrium (2010, background): “In particular, can it be true that the entropy is associated with the area of the apparent horizon? The fact that CFT entropy is not determined by the area of the event horizon in general is perhaps not so surprising, given that the event (60)More recently [224] argue that a Wilson renormalization g”