TY - JOUR

T1 - The incompressible Navier-Stokes equations from black hole membrane dynamics

AU - Eling, Christopher

AU - Fouxon, Itzhak

AU - Oz, Yaron

N1 - Funding Information:
The work of I.F. and Y.O. is supported in part by the Israeli Science Foundation center of excellence, by the Deutsch–Israelische Projektkooperation (DIP) , by the US–Israel Binational Science Foundation (BSF) , and by the German–Israeli Foundation (GIF) . C.E. is supported by the Lady Davis Foundation at Hebrew University and by grant 694/04 of the Israel Science Foundation , established by the Israel Academy of Sciences and Humanities.

PY - 2009/10/12

Y1 - 2009/10/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70349419603&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2009.09.028

DO - 10.1016/j.physletb.2009.09.028

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AN - SCOPUS:70349419603

SN - 0370-2693

VL - 680

SP - 496

EP - 499

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 5

ER -