Towards the uniqueness of Lifshitz black holes and solitons in New Massive Gravity

TL;DR

This paper proves the uniqueness of certain Lifshitz black hole and soliton solutions in New Massive Gravity, highlighting special values of the dynamical critical exponent z and their significance.

Contribution

It establishes the uniqueness of z=1 and z=3 Lifshitz black holes and z=1 and z=1/3 Lifshitz solitons in three-dimensional New Massive Gravity.

Findings

z=1 and z=3 Lifshitz black holes are the only static axisymmetric solutions in Kerr-Schild form.

z=1 and z=1/3 Lifshitz solitons are the only solutions within a specific ansatz.

The approach explains the special nature of these z values at finite temperature.

Abstract

We prove that the z=1 and z=3 Lifshitz black hole solutions of New Massive Gravity in three dimensions are the only static axisymmetric solutions that can be cast in a Kerr-Schild form with a seed metric given by the Lifshitz spacetime. Correspondingly, we study the issue of uniqueness of Lifshitz solitons when considering an ansatz involving a single metric function. We show this problem can be mapped to the previous one and that the z=1 and z=1/3 Lifshitz soliton solutions are the only ones within this class. Finally, our approach suggests for the first time an explanation as to what is special about those particular values of the dynamical critical exponent z at finite temperature.