Fluid/Gravity Correspondence For General Non-rotating Black Holes

TL;DR

This paper explores the fluid/gravity duality for non-rotating black holes, deriving a generalized Navier-Stokes equation for the dual fluid, which simplifies under stationary conditions, advancing understanding of black hole holography.

Contribution

It introduces a generalized fluid description for non-rotating black holes using Petrov-like boundary conditions and large mean curvature limits, extending the fluid/gravity correspondence.

Findings

Derivation of a generalized forced incompressible Navier-Stokes equation

Reduction to standard Navier-Stokes for stationary black holes

Application of Petrov-like boundary conditions in non-rotating horizons

Abstract

In this paper, we investigate the fluid/gravity correspondence in spacetime with general non-rotating weakly isolated horizon. With the help of Petrov-like boundary condition and large mean curvature limit, we show that the dual hydrodynamical system is described by a generalized forced incompressible Navier-Stocks equation. Specially, for stationary black holes or those spacetime with some asymptotically stationary conditions, such a system reduces to a standard forced Navier-Stocks system.