Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP04(2015)136
Keywords
Gauge-gravity correspondence; AdS-CFT Correspondence; Holography and quark-gluon plasmas
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Funding
- ISRAELI SCIENCE FOUNDATION [87277111]
- BSF [012124]
- People Program (Marie Curie Actions) of the European Union's Seventh Framework under REA [318921]
- Council for Higher Education of Israel
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We extend our study of all-order linearly resummed hydrodynamics in a flat space [1, 2] to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature N = 4 super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically locally AdS(5) geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid's energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs. [1, 2], we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref. [3], the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.
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