The incompressible Navier-Stokes equations from black hole membrane dynamics

Christopher Eling*, Itzhak Fouxon, Yaron Oz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the dynamics of a d + 1 space-time dimensional membrane defined by the event horizon of a black brane in (d + 2)-dimensional asymptotically Anti-de Sitter space-time and show that it is described by the d-dimensional incompressible Navier-Stokes equations of non-relativistic fluids. The fluid velocity corresponds to the normal to the horizon while the rate of change in the fluid energy is equal to minus the rate of change in the horizon cross-sectional area. The analysis is performed in the Membrane Paradigm approach to black holes and it holds for a general non-singular null hypersurface, provided a large scale hydrodynamic limit exists. Thus we find, for instance, that the dynamics of the Rindler acceleration horizon is also described by the incompressible Navier-Stokes equations. The result resembles the relation between the Burgers and KPZ equations and we discuss its implications.

Original languageEnglish
Pages (from-to)496-499
Number of pages4
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Issue number5
StatePublished - 12 Oct 2009


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