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

Understand

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.