More on New Massive Gravity: Exact Solutions

TL;DR

This paper provides a new framework for understanding and generating exact solutions in three-dimensional new massive gravity (NMG), connecting it to topologically massive gravity (TMG) and presenting novel solutions.

Contribution

It introduces a novel description of NMG using a Dirac-type operator, linking TMG solutions to NMG, and presents new exact solutions unique to NMG.

Findings

Mapped TMG algebraic solutions to NMG

Developed a framework for exact solutions in NMG

Discovered new algebraic type D and N solutions

Abstract

We give a novel description of the recently proposed theory of new massive gravity (NMG) in three dimensions. We show that in terms of a Dirac type differential operator acting on the traceless Ricci tensor, the field equations of the theory reduce to the massive Klein-Gordon type equation with a curvature-squared source term and to a constraint equation. Under a certain relation between the source tensor and the traceless Ricci tensor, fulfilled for constant scalar curvature, the field equations of topologically massive gravity (TMG) can be thought of as the "square-root" of the massive Klein-Gordon type equation. Using this fact, we establish a simple framework for mapping all known algebraic types D and N solutions of TMG into NMG. We also present new exact solutions of algebraic types D and N which are only inherent in NMG.