Supersymmetric Backgrounds and Black Holes in ${\cal N}=(1,1)$ Cosmological New Massive Supergravity

TL;DR

This paper systematically investigates supersymmetric backgrounds and black hole solutions in the ${ m N}=(1,1)$ Cosmological New Massive Supergravity, revealing new solutions and analyzing their properties.

Contribution

It introduces new supersymmetric solutions with time-like Killing vectors, including Lifshitz spacetimes, and analyzes the supersymmetry of various black holes in this model.

Findings

Null Killing vector solutions are pp-waves similar to ${ m N}=1$ model.

New solutions with time-like Killing vectors, such as Lifshitz spacetime.

No supersymmetric Lifshitz black hole solutions under certain conditions.

Abstract

Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the ${\cal N}=(1,1)$ Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the ${\cal N}=1$ model but we find new solutions with a time-like Killing vector that are absent in the ${\cal N}=1$ case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the so-called rotating hairy BTZ black holes and logarithmic black holes in an $AdS_3$ background. Furthermore, we show that under certain assumptions there is no supersymmetric Lifshitz black hole solution.