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.

arXiv comment10 pages, 5 figures

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Cited by in corpus (20)

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• Regular black holes in three dimensions
• First law and anisotropic Cardy formula for three-dimensional Lifshitz black holes
• Ruppeiner Geometry, Phase Transitions and Microstructures of Black Holes in Massive Gravity
• Asymptotically locally flat spacetimes and dynamical black flowers in three dimensions
• Causality in 3D Massive Gravity Theories
• Novel relations in massive gravity at Hawking-Page transition
• Microscopic entropy of higher-dimensional nonminimally dressed Lifshitz black holes
• Thermodynamics and Cardy-like formula for nonminimally dressed, charged Lifshitz black holes in New Massive Gravity
• 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
• On regular charged black holes in three dimensions
• Anisotropic Scale Invariant Spacetimes and Black Holes in Zwei-Dreibein Gravity
• Static spheres and Aschenbach effect for black holes in massive gravity
• Asymptotically flat black holes and gravitational waves in three-dimensional massive gravity
• Topological charge and black hole photon spheres in massive gravity
• Weyl double copy in Lifshitz spacetimes
• Lifshitz black holes in four-dimensional Critical Gravity
• The mass of a Lifshitz black hole