Effective hydrodynamics of black D3-branes

TL;DR

This paper demonstrates that the long-wavelength fluctuations of black D3-branes can be described as a hydrodynamical system, connecting gravitational dynamics with fluid behavior across different regimes and unifying various theoretical approaches.

Contribution

It shows that the effective field theory of black D3-branes' fluctuations is a hydrodynamical system, bridging non-conformal and conformal fluids and unifying blackfold, fluid/gravity, and membrane paradigms.

Findings

Interpolates between non-conformal and conformal fluids.

Recovers known fluid descriptions in near-extremal limit.

Provides a universal framework for black brane dynamics.

Abstract

The long-wavelength effective field theory of world-volume fluctuations of black D3-branes is shown to be a hydrodynamical system to leading order in a gradient expansion. We study the system on a fiducial `cutoff' surface: the fluctuating geometry imprints its dynamics on the surface via an induced stress tensor whose conservation encapsulates the hydrodynamical description. For a generic non-extremal D3-brane, as we move our cutoff surface from the asymptotically flat near-boundary region to the near-horizon region, this hydrodynamical system interpolates between a non-conformal relativistic fluid and a non-relativistic incompressible fluid. We also consider the dependence on the deviation from extremality of the D3-branes. In the near-extremal case we recover the description in terms of a conformal relativistic fluid encountered in the AdS/CFT context. We argue that this system allows us therefore to explore the various connections that have hitherto been suggested relating the dynamics of gravitational systems and fluid dynamics. In particular, we go on to show that the blackfold effective field theory approach allows us to capture this hydrodynamical behaviour and moreover subsumes the constructions encountered in the fluid/gravity correspondence and the black hole membrane paradigm, providing thereby a universal language to explore the effective dynamics of black branes.