Hysteresis in $$\eta /s$$ η / s for QFTs dual to spherical black holes

Abstract

We define and compute the (analog) shear viscosity to entropy density ratioη/s for the QFTs dual to spherical AdS black holes both in Einstein and Gauss-Bonnet gravity in five spacetime dimensions. Although in this case, owing to the lack of translational symmetry of the background,η does not have the usual hydrodynamic meaning, it can be still interpreted as the rate of entropy production due to a strain. At large and small temperatures it is found thatη/s is a monotonic increasing function of the temperature. In particular, at large temperatures it approaches a constant value, whereas at small temperatures, when the black hole has a regular, stable extremal limit,η/s goes to zero with scaling law behavior. Whenever the phase diagram of the black hole has a Van der Waals-like behavior, i.e. it is characterized by the presence of two stable states (small and large black holes), connected by a meta-stable region (intermediate black holes), the system evolution must occur through the meta-stable regionand temperature-dependent hysteresis ofη/s is generated by non-equilibrium thermodynamics.

Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling

“…The regime of weak coupling can be described by the kinetic theory, while the transition from weak to strong coupling, i. e., the regime of intermediate coupling is not yet understood. Recently, an approach allowing one to obtain corrections to the regime of infinite coupling has been suggested in [10][11][12][13]. There it is shown that higher curvature corrections to the gravitational action, such as the GaussBonnet, Lovelock, R 4 or other terms, may give us a hint on what happens in the regime of intermediate coupling.…”

Van der Waals-like behaviour of charged black holes and hysteresis in the dual QFTs

“…Detailed calculations and generalisation to Gauss-Bonnet neutral and charged black holes are presented in Ref. [26].…”