Black Hole Dynamics From Atmospheric Science

TL;DR

This work extends the fluid/gravity correspondence to 2+1 Dimensional boundary fluids by deriving a 3+1D AdS gravity dual for long-wavelength perturbations of a black brane, using a derivative expansion up to second order in velocity gradients. The author constructs the dual geometry perturbatively, obtains the covariant metric to second order, and computes the boundary stress tensor, revealing explicit second-order transport coefficients, including a new $\lambda_2$. The analysis highlights potential qualitative differences between 4D and 5D black hole dynamics due to 2+1 turbulence and discusses implications for AdS/CFT applications, including neutral and potentially charged fluids in various holographic CFTs. Overall, the paper provides a concrete, higher-order gravity realization of relativistic hydrodynamics in a lower-dimensional boundary theory with direct links to turbulence and holography.

Abstract

In this note, we derive (to third order in derivatives of the fluid velocity) a 2+1 dimensional theory of fluid dynamics that governs the evolution of generic long-wavelength perturbations of a black brane or large black hole in four-dimensional gravity with negative cosmological constant, applying a systematic procedure developed recently by Bhattacharyya, Hubeny, Minwalla, and Rangamani. In the regime of validity of the fluid-dynamical description, the black-brane evolution will generically correspond to a turbulent flow. Turbulence in 2+1 dimensions has been well studied analytically, numerically, experimentally, and observationally as it provides a first approximation to the large scale dynamics of planetary atmospheres. These studies reveal dramatic differences between fluid flows in 2+1 and 3+1 dimensions, suggesting that the dynamics of perturbed four and five dimensional large AdS black holes may be qualitatively different. However, further investigation is required to understand whether these qualitative differences exist in the regime of fluid dynamics relevant to black hole dynamics.