The General Type N Solution of New Massive Gravity

TL;DR

This paper derives the most general algebraic type N solutions with non-zero scalar curvature in new massive gravity, revealing special cases related to critical topological mass and AdS pp-waves.

Contribution

It provides the complete algebraic type N solutions for new massive gravity in three dimensions, including special cases with restored null Killing isometry.

Findings

Derived the general algebraic type N solutions with non-zero scalar curvature.

Identified special solutions corresponding to critical topological mass values.

Showed that at the critical limit, solutions describe AdS pp-waves with null Killing isometry.

Abstract

We find the most general algebraic type N solution with non-vanishing scalar curvature, which comprises all type N solutions of new massive gravity in three dimensions. We also give the special forms of this solution, which correspond to certain critical values of the topological mass. Finally, we show that at the special limit, the null Killing isometry of the spacetime is restored and the solution describes AdS pp-waves.