On Charged Lifshitz Black Holes

TL;DR

This paper derives exact charged Lifshitz black hole solutions in various dimensions, explores their thermodynamics, and investigates transport properties with Gauss-Bonnet corrections, highlighting challenges in defining mass in non-relativistic backgrounds.

Contribution

It provides new exact solutions for charged Lifshitz black holes in arbitrary dimensions and analyzes their thermodynamic and transport properties with higher-curvature corrections.

Findings

Mass cannot be defined by standard methods, only via the first law.

Exact solutions are obtained in arbitrary dimensions.

Transport coefficients are computed with Gauss-Bonnet corrections.

Abstract

We obtain exact solutions of charged asymptotically Lifshitz black holes in arbitrary (d+2) dimensions, generalizing the four dimensional solution investigated in 0908.2611[hep-th]. We find that both the conventional Hamiltonian approach and the recently proposed method for defining mass in non-relativistic backgrounds do not work for this specific example. Thus the mass of the black hole can only be determined by the first law of thermodynamics. We also obtain perturbative solutions in five-dimensional Gauss-Bonnet gravity. The ratio of shear viscosity over entropy density and the DC conductivity are calculated in the presence of Gauss-Bonnet corrections.