An analytic Lifshitz black hole

TL;DR

This paper constructs an exact Lifshitz black hole solution, analyzes its thermodynamics and scalar responses, and finds that its Green's functions differ from free Lifshitz scalar theories, providing new insights into holographic duals.

Contribution

It analytically constructs a Lifshitz black hole solution and studies its properties, extending previous models with exact solutions and novel scalar response behavior.

Findings

Exact Lifshitz black hole solution obtained

Scalar wave equation is exactly solvable

Green's functions differ from free Lifshitz scalar theory

Abstract

A Lifshitz point is described by a quantum field theory with anisotropic scale invariance (but not Galilean invariance). In arXiv:0808.1725, gravity duals were conjectured for such theories. We construct analytically a black hole which asymptotes to a vacuum Lifshitz solution; this black hole solves the equations of motion of some simple (but somewhat strange) extensions of the models of arXiv:0808.1725. We study its thermodynamics and scalar response functions. The scalar wave equation turns out to be exactly solvable. Interestingly, the Green's functions do not exhibit the ultralocal behavior seen previously in the free Lifshitz scalar theory.