A Note on Black Holes in Asymptotically Lifshitz Spacetime

TL;DR

This paper analyzes exact black hole solutions in asymptotically Lifshitz spacetime, examining tidal forces, Wilson loops, and hydrodynamic properties, revealing universal ratios and bounds in various dimensions.

Contribution

It provides detailed calculations of tidal forces, Wilson loops, shear viscosity, and sound speed in Lifshitz black holes, highlighting universal behaviors and bounds.

Findings

Tidal forces diverge near extremal horizons.

Wilson loops computed for extremal and finite temperature cases.

Shear viscosity to entropy density ratio is universally 1/4π.

Abstract

We investigate several aspects of exact black hole solutions in asymptotically Lifshitz spacetime, which were proposed in 0812.0530. Firstly, we calculate the tidal forces and find that in the near horizon region of such black hole backgrounds, the tidal forces diverge in the near extremal limit. Secondly, we evaluate the Wilson loops in both extremal and finite temperature cases. Finally, we obtain the corresponding shear viscosity and square of the sound speed and find that the ratio of shear viscosity to entropy density takes the universal value $1/4\pi$ in arbitrary dimensions while the square of the speed of sound saturates the conjectured bound 1/3 in five dimensions.