Classical Aspects of Higher Spin Topologically Massive Gravity

TL;DR

This paper explores classical solutions of three-dimensional higher spin topologically massive gravity, including AdS pp-waves with higher spin hair and warped spacetimes, using a Chern-Simons-like formulation and introducing special Killing vectors.

Contribution

It provides the first analysis of classical solutions in higher spin TMG, including new AdS pp-wave solutions and a framework for warped spacetimes using special Killing vectors.

Findings

Higher spin fields can modify pp-wave geometries.

Reproduced various warped spacetimes within the higher spin TMG framework.

Established a method to analyze solutions using special Killing vectors.

Abstract

We study the classical solutions of three dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first order formulation. The action of higher spin TMG has been proposed in arXiv:1110.5113 to be of a Chern-Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS$_3$ gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair, and find that the nonvanishing higher spin fields may or may not modify the pp-wave geometry. In order to discuss the warped spacetime, we introduce the notion of special Killing vector, which is defined to be the symmetry on the frame-like fields. We reproduce various warped spacetimes of TMG in our framework, with the help of special Killing vectors.