TY - JOUR

T1 - The shear diffusion coefficient for generalized theories of gravity

AU - Brustein, Ram

AU - Medved, A. J.M.

N1 - Funding Information:
The research of R.B. was supported by The Israel Science Foundation grant no 470/06. The research of A.J.M.M. is supported by the University of Seoul.

PY - 2009/1/12

Y1 - 2009/1/12

N2 - Near the horizon of a black brane in Anti-de Sitter (AdS) space and near the AdS boundary, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. The gauge-gravity duality then relates the boundary hydrodynamics for generalized gravity to that of gauge theories with large finite values of 't Hooft coupling. We discuss, for this framework, the hydrodynamics of the shear mode in generalized theories of gravity in d + 1 dimensions. It is shown that the shear diffusion coefficients of the near-horizon and boundary hydrodynamics are equal and can be expressed in a form that is purely local to the horizon. We find that the Einstein-theory relation between the shear diffusion coefficient and the shear viscosity to entropy ratio is modified for generalized gravity theories: Both can be explicitly written as the ratio of a pair of polarization-specific gravitational couplings but implicate differently polarized gravitons. Our analysis is restricted to the shear-mode fluctuations for simplicity and clarity; however, our methods can be applied to the hydrodynamics of all gravitational and matter fluctuation modes.

AB - Near the horizon of a black brane in Anti-de Sitter (AdS) space and near the AdS boundary, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. The gauge-gravity duality then relates the boundary hydrodynamics for generalized gravity to that of gauge theories with large finite values of 't Hooft coupling. We discuss, for this framework, the hydrodynamics of the shear mode in generalized theories of gravity in d + 1 dimensions. It is shown that the shear diffusion coefficients of the near-horizon and boundary hydrodynamics are equal and can be expressed in a form that is purely local to the horizon. We find that the Einstein-theory relation between the shear diffusion coefficient and the shear viscosity to entropy ratio is modified for generalized gravity theories: Both can be explicitly written as the ratio of a pair of polarization-specific gravitational couplings but implicate differently polarized gravitons. Our analysis is restricted to the shear-mode fluctuations for simplicity and clarity; however, our methods can be applied to the hydrodynamics of all gravitational and matter fluctuation modes.

UR - http://www.scopus.com/inward/record.url?scp=57749118699&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2008.11.038

DO - 10.1016/j.physletb.2008.11.038

M3 - Article

AN - SCOPUS:57749118699

VL - 671

SP - 119

EP - 122

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

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

SN - 0370-2693

IS - 1

ER -