## $$\mathrm{AdS}_5$$-Schwarzschild deformed black branes and hydrodynamic transport coefficients.(English)Zbl 1473.83046

Summary: A family of deformed $$\mathrm{AdS}_5$$-Schwarzschild black branes is here derived, employing the membrane paradigm of AdS/CFT. The solution of the Einstein-Hilbert action, with the Gibbons-Hawking term and a counter-term that eliminates eventual divergences, yields a partition function associated to the dual theory which allows the computation of the entropy, pressure and free energy, as state functions, in the canonical ensemble. AdS/CFT near-horizon methods are then implemented to compute the shear viscosity-to-entropy ratio, then restricting the range of the parameter that defines a family of deformed black branes.

### MSC:

 83C57 Black holes 83C15 Exact solutions to problems in general relativity and gravitational theory 14D15 Formal methods and deformations in algebraic geometry 81T35 Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) 83C56 Dark matter and dark energy 83E30 String and superstring theories in gravitational theory 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) 76E20 Stability and instability of geophysical and astrophysical flows
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