A fluid dual to charged large D membrane paradigm

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.