A note on gravity and fluid dynamic correspondence on a null hypersurface

TL;DR

This work extends the fluid–gravity correspondence to generic null surfaces by constructing a Brown–York–like energy–momentum tensor intrinsic to the null boundary. By expressing the null BY tensor in terms of conjugate momenta to the two-mmetric q^{ab} and the null normal l^a, the authors derive a complete fluid dictionary: energy density, momentum density, and stress map to a 2D viscous null fluid, and the Damour–Navier–Stokes, Raychaudhuri, and continuity-like relations arise from covariant EMT conservation. They identify the fluid parameters (η, ζ, P) and thermodynamics (T, entropy) and demonstrate consistency with the KSS bound and Bekenstein–Hawking entropy, with explicit checks in Schwarzschild, Kerr, and FRW spacetimes. The approach avoids divergences associated with stretched horizons and strengthens the emergent gravity program by providing a covariant, null-foliation–based fluid description of gravitational dynamics on null hypersurfaces, including a non-relativistic limit. The work also situates its results in relation to Carrollian and membrane paradigms and discusses implications for asymptotic null infinity and Bondi data.

Abstract

In the extensive literature on fluid-gravity correspondence formulated on null hypersurfaces, the Carrollian and membrane paradigm approaches have predominantly employed a timelike foliation. By contrast, within the null foliation formalism, only the momentum conservation law, expressed through the Damour-Navier-Stokes (DNS) equation, has been established. In this work, we revisit the null foliation formalism for a generic null hypersurface and extend it to include the energy conservation law, continuity equation, and related relations, all derived from the covariant conservation of an appropriately defined energy-momentum tensor. This development complements the existing literature on the fluid description of gravitational dynamics in the null foliation framework.