Classical Aspects of Higher Spin Topologically Massive Gravity

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.

25 pages; minor corrections, references added, published version

References in corpus (5)

• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Warped AdS_3 Black Holes
• Towards non-AdS holography in 3-dimensional higher spin gravity
• High Spin Topologically Massive Gravity
• All stationary axi-symmetric local solutions of topologically massive gravity

Cited by in corpus (7)

• Charged black hole with a scalar hair in (2+1) dimensions
• New Unfolded Higher Spin Systems in $Ad{S}_3$
• Black holes in Truncated Higher Spin AdS${}_3$ Gravity
• Topologically massive higher spin gauge theories
• Holographic Renormalisation for the Spin-3 Theory and the (A)dS3/CFT2 correspondence
• New class of rotating perfect fluid black holes in three dimensional gravity
• Asymptotic symmetries of three-dimensional higher-spin gravity: the metric approach