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

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.

10 pages, 5 figures

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• Regular BTZ black holes from an infinite tower of corrections
• Electromagnetic Generalized Quasi-topological gravities in $(2+1)$ dimensions
• Critical Heat Engines in Massive Gravity
• Anisotropic Scale Invariant Spacetimes and Black Holes in Zwei-Dreibein Gravity
• On regular charged black holes in three dimensions
• Static spheres and Aschenbach effect for black holes in massive gravity
• Weyl double copy in Lifshitz spacetimes
• Lifshitz black holes in four-dimensional Critical Gravity
• The mass of a Lifshitz black hole
• Topological charge and black hole photon spheres in massive gravity