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

Abstract

We investigate black brane solutions in asymptotically Lifshitz spacetime in 3+1-dimensional Horndeski gravity, which parameters are related to the cosmological constant as \(\alpha=\gamma\Lambda\) and depend on arbitrary values of the dynamical critical exponent \(z\) since \(\Lambda=-(1+2z)/L^{2}\). For the case \(z=1\) we recover black brane solutions in asymptotically AdS\(_{4}\) spacetime. We also investigate the shear viscosity in the 2+1-dimensional 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 \(\eta/s\geq1/(4\pi)\) is violated.