AdS$_5$-Schwarzschild deformed black branes and hydrodynamic transport coefficients

TL;DR

This paper derives a family of deformed AdS$_5$-Schwarzschild black branes using the membrane paradigm of AdS/CFT, enabling the calculation of thermodynamic properties and hydrodynamic transport coefficients.

Contribution

It introduces a novel family of deformed black brane solutions and computes their thermodynamic and hydrodynamic transport properties within the AdS/CFT framework.

Findings

Derived explicit deformed black brane solutions.

Computed entropy, pressure, and free energy as state functions.

Calculated shear viscosity-to-entropy ratio for the deformed solutions.

Abstract

A family of deformed 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 with 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.