Type D Solutions of 3D New Massive Gravity

TL;DR

This paper classifies all algebraic type D solutions of three-dimensional new massive gravity, including homogeneous, conformally flat, and black hole solutions, using a reformulated field equation framework.

Contribution

It provides a complete classification of algebraic type D solutions in NMG, including new solutions and their properties, expanding understanding of the theory's solution space.

Findings

Includes solutions from TMG and non-TMG origins.

Identifies conformally flat solutions at mbda=m^2.

Finds metrics with at least one Killing vector, including black hole solutions.

Abstract

In a recent reformulation of three-dimensional new massive gravity (NMG), the field equations of the theory consist of a massive (tensorial) Klein-Gordon type equation with a curvature-squared source term and a constraint equation. Using this framework, we present all algebraic type D solutions of NMG with constant and nonconstant scalar curvatures. For constant scalar curvature, they include homogeneous anisotropic solutions which encompass both solutions originating from topologically massive gravity (TMG), Bianchi types II, VIII, IX, and those of non-TMG origin, Bianchi types VI_{0} and VII_{0} . For a special relation between the cosmological and mass parameters, \lambda=m^2, they also include conformally flat solutions, and in particular those being locally isometric to the previously-known Kaluza-Klein type AdS_2xS^1 or dS_2x S^1 solutions. For nonconstant scalar curvature, all the solutions are conformally flat and exist only for \lambda=m^2 . We find two general metrics which possess at least one Killing vector and comprise all such solutions. We also discuss some properties of these solutions, delineating among them black hole type solutions.