Black brane in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity

Abstract

We investigate black brane solutions in asymptotically Lifshitz spacetime in 3+1dimensional Horndeski gravity, which parameters are related to the cosmological constant as α = γΛ and depend on arbitrary values of the dynamical critical exponent z since Λ = −(1 + 2z)/L 2 . For the case z = 1 we recover black brane solutions in asymptotically AdS 4 spacetime. We also investigate the shear viscosity in the 2+1dimensional dual boundary field theory via holographic correspondence. We show that for arbitrary values of AdS radius L, only two specific critical exponents are allowed: z = −0.3 or z = 3.3. At the former value, we find that the bound for viscosity to entropy density ratio η/s ≥ 1/(4π) is violated.

Complexity of four-dimensional hairy anti-de-Sitter black holes with a rotating string and shear viscosity in generalized scalar–tensor theories

“…In fact, if we suppose that for the spherical case the mass M = M/(2Z 1 2,1 ) is fixed, yet we can change the values of L from ( 27) with a suitable election of the coupling functions satisfy (21), given in the Fig. 5.…”

“…On the other hand, anti-de-Sitter (AdS) planar black holes allow us to analyze the effects on shear viscosity, thanks to the gravity/gauge duality [17][18][19] and by effective coupling constants of the transverse graviton on the location of the event horizon [20], where the fluid is characterized by the production of entropy [21]. For some common substances (for example helium, nitrogen, and water) the viscosity/entropy density (η/s) ratio is always substantially greater than its value in dual gravity theories, which reads as [22][23][24] η…”

“…This value has been shown in a variety of cases (see [25][26][27][28]). However, there are concrete examples where the KSS bound (2) is violated, for example, via gravitational theories such as the five-dimensional Einstein-Hilbert Gauss-Bonnet model [29,30] as well as scalar-tensor theories [21,31], where the Lagrangian is given by (1).…”

Modeling Dark Sector in Horndeski Gravity at First-Order Formalism

“…In our present investigation, we shall address the study of Friedmann-Robertson-Walker (FRW) solutions in the framework of the Horndeski gravity [15][16][17][18][19][20] which action with a scalar potential reads…”

“…Recent investigations about Einstein gravity have called attention for the coupling of the theory to scalar fields [18]. These efforts led to the development of the well-known Galileons that are scalar-tensor theories [14].…”