Hydrodynamics of a black brane in Gauss–Bonnet massive gravity

Abstract

A black brane solution to a Gauss-Bonnet massive gravity is introduced. In the context of AdS/CFT correspondence, the viscosity to entropy ratio is found by the Green-Kubo formula. The result indicates violation of the well-known KSS bound as expected in a higher derivative theory. Setting mass zero gives back the known viscosity to entropy ratio dependent on the Gauss-Bonnet coupling, while without Gauss-Bonnet term, a nonzero mass parameter doesn't contribute to the ratio which saturates the bound of 1 4π .

Einstein–Yang–Mills AdS black brane solution in massive gravity and viscosity bound

“…The Petrov-like boundary [29] condition on the hypersurface preserves KSS bound but the Dirichlet boundary and regularity on the horizon conditions violate KSS bound [28]. We showed that our result (40) is in agreement to the literature and it is valid perturbatively in m and e. When the KSS bound violates it means the model behaves effectively like higher derivative gravity theories [27,30,31,32,33] and when the KSS bound saturates it means the model behaves effectively like Einstein-Hilbert gravity.…”

Note on the Noether charge and holographic transports

“…The AdS/CFT correspondence provides a new powerful method to compute the transport coefficients of strongly coupled systems that live on the boundary of asymptotically anti-de Sitter (AdS) space-times, including the ratio of shear viscosity to entropy density [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] and thermal-electric conductivities (for nice reviews, see [19,20,21]). This is achieved by analysing small perturbations about the black holes background which describe the equilibrium state at finite temperature and chemical potential.…”

Transverse shear viscosity to entropy density for the general anisotropic black brane in Horava–Lifshitz gravity

“…The massive term with the Dirichlet boundary condition and regularity on the horizon [25,26,27] violate the KSS bound but the massive term with the Petrov-like boundary condition preserve this bound [28]. However, this conjecture violates for higher derivative gravities [29,30,31,32,33,34,35,36,37,38,39,40].…”