A leading-order comparison between fluid-gravity and membrane-gravity dualities

Abstract

In this note, we have compared two different perturbation techniques that are used to generate dynamical black-brane solutions to Einstein equation in presence of negative cosmological constant. One is the `derivative expansion', where the gravity solutions are in one-to-one correspondence with the solutions of relativistic Navier-Stokes equation. The second is the expansion in terms of inverse power of space-time dimensions and here the gravity solutions are dual to a co-dimension one dynamical membrane, embedded in AdS space and coupled to a velocity field. We have shown that in large number of space-time dimensions, there exists an overlap regime between these two perturbation techniques and we matched the two gravity solutions along with their dual systems upto the first non-trivial order in the expansion parameter on both sides. In the process, we established a one-to-one map between dynamical black-brane geometry and the AdS space, which exists even when the number of dimensions is finite.

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References in corpus (23)

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• Fluid dynamics of R-charged black holes
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• Large D gravity and low D strings
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• The large D black hole Membrane Paradigm at first subleading order
• Unstable `black branes' from scaled membranes at large $D$
• Holographic Turbulence in a Large Number of Dimensions
• An Action for and Hydrodynamics from the improved Large D membrane
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• Black holes in presence of cosmological constant: Second order in 1/D
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Cited by in corpus (6)

• The Large D Limit of Einstein's Equations
• Large D membrane for Higher Derivative Gravity and Black Hole Second Law
• The large $D$ membrane paradigm for general four-derivative theory of gravity with a cosmological constant
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• Black Hole Critical Collapse in Infinite Dimensions: Continuous Self-Similar Solutions
• Stress Tensor for Large-$D$ membrane at subleading orders