Homogeneous vacua of (generalized) new massive gravity

TL;DR

This paper classifies all homogeneous solutions of new massive gravity on S^3 and AdS_3, revealing various symmetric and anisotropic vacua, and explores transitions among them via instantons in Horava-Lifshitz gravity.

Contribution

It extends the classification of homogeneous vacua in new massive gravity to include axially symmetric and anisotropic solutions, and models their transitions using instantons in higher-dimensional gravity.

Findings

All homogeneous solutions on S^3 and AdS_3 are classified.

Existence of axially symmetric and anisotropic vacua beyond maximally symmetric ones.

Transitions among vacua are described by instantons in 3+1 Horava-Lifshitz gravity.

Abstract

We obtain all homogeneous solutions of new massive gravity models on S^3 and AdS_3 by extending previously known results for the cosmological topologically massive theory of gravity in three dimensions. In all cases, apart from the maximally symmetric vacua, there are axially symmetric (i.e., bi-axially squashed) as well as totally anisotropic (i.e., tri-axially squashed) metrics of special algebraic type. Transitions among the vacua are modeled by instanton solutions of 3+1 Horava-Lifshitz gravity with anisotropic scaling parameter z=4.