All stationary axi-symmetric local solutions of topologically massive gravity

TL;DR

This paper classifies all stationary axi-symmetric solutions of topologically massive gravity, explicitly constructing some and providing an algorithm for numerical solutions in the generic case, with applications to solitons and warped AdS.

Contribution

It provides a complete classification and explicit construction of solutions, along with a numerical algorithm for the generic sector of topologically massive gravity.

Findings

Explicit solutions for Einstein, Schrödinger, and warped sectors

An algorithm for numerical solutions in the generic sector

Examples including solitons asymptoting to warped AdS

Abstract

We classify all stationary axi-symmetric solutions of topologically massive gravity into Einstein, Schr\"odinger, warped and generic solutions. We construct explicitly all local solutions in the first three sectors and present an algorithm for the numerical construction of all local solutions in the generic sector. The only input for this algorithm is the value of one constant of motion if the solution has an analytic centre, and three constants of motion otherwise. We present several examples, including soliton solutions that asymptote to warped AdS.