A fluid dual to charged large D membrane paradigm

TL;DR

This paper establishes a duality between the dynamics of charged black hole membranes in large D gravity and relativistic charged fluids, revealing unique transport properties and stability mechanisms.

Contribution

It introduces a fluid dual to charged black hole membranes in large D gravity, extending the membrane paradigm beyond AdS spacetimes.

Findings

The dual fluid exhibits negative thermal conductivity and heat capacity.

The stability of the system aligns with quasinormal mode damping.

The correspondence applies to asymptotically flat black holes with specific fluid systems.

Abstract

According to the formulation of the charged large $D$ membrane paradigm, an arbitrary dynamic black hole solution to a theory of gravity with a $U(1)$ gauge field is dual to the dynamics of a membrane in a non-gravitational background. This membrane is endowed with a stress-energy tensor and a charge current, whose conservation equations govern its dynamics. In this work, we demonstrate that the dynamics of these membrane configurations (at the leading nontrivial order in $1/D$) can be mapped to a relativistic charged fluid. Establishing a correspondence for asymptotically flat black holes with a particular class of fluid systems. Unlike the standard AdS/Hydrodynamics correspondence, this dual fluid does not reside on an asymptotic boundary, but is localized strictly on the non-gravitational membrane worldvolume. By evaluating the system in both the Eckart and Landau frames, we systematically extract the out-of-equilibrium transport coefficients. We find that the fluid is governed by a negative effective thermal conductivity and a negative heat capacity, a mechanism that enforces thermodynamic stability in agreement with the quasinormal mode damping in the large $D$ Reissner-Nordstr\"om black hole geometry.