Unstable `black branes' from scaled membranes at large $D$

Abstract

It has recently been demonstrated that the dynamics of black holes at large $D$ can be recast as a set of non gravitational membrane equations. These membrane equations admit a simple static solution with shape $S^{D-p-2}\times R^{p,1}$. In this note we study the equations for small fluctuations about this solution in a limit in which amplitude and length scale of the fluctuations are simultaneously scaled to zero as $D$ is taken to infinity. We demonstrate that the resultant nonlinear equations, which capture the Gregory- Laflamme instability and its end point, exactly agree with the effective dynamical `black brane' equations of Emparan Suzuki and Tanabe. Our results thus identify the `black brane' equations as a special limit of the membrane equations and so unify these approaches to large $D$ black hole dynamics.

10 pages, references added

References in corpus (2)

• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• On Brane Instabilities in the Large $D$ Limit

Cited by in corpus (6)

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• Fluid-gravity and membrane-gravity dualities - Comparison at subleading orders
• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
• An analytic approach for holographic entanglement entropy at (quantum) criticality