D2 Chern-Simons Gravity

TL;DR

This paper explores a two spin-2 field gravity theory in AdS3, constructing black holes and analyzing their thermodynamics, revealing insights into higher spin gravity and bi-gravity formulations.

Contribution

It introduces a simplified higher spin gravity model with two spin-2 fields, constructs black holes, and connects their thermodynamics to bi-gravity frameworks.

Findings

Black holes with spin-2 hair are constructed and analyzed.

The action can be reformulated as an AdS3 bi-gravity model.

Black hole entropy matches bi-gravity calculations.

Abstract

We study the theory that contains two spin-2 fields. This theory can be regarded as a simplified version of higher spin gravity in AdS3. It can be formulated either in the first order formulation or in the second order formulation. From the first order formulation we construct the black holes in the theory and study the thermodynamics of this black holes with the help of dual holographic OPE. From the higher spin point of view, this black hole is most naturally regarded as a black hole with a spin-2 hair. In the second order formulation, we obtain an action for the metric and extra spin-2 fields and analyze the corresponding black holes. Even though for some simple cases, the conventional notions, such as the horizon, may help us to read part of the information of the black hole, they break down in generic cases. On the other hand, the action in the second order formulation could be rewritten in the form of a decoupled AdS3 bi-gravity. Moreover, the entropy of the black hole with the spin-2 hair could be reproduced from the AdS3 bi-gravity in the Euclidean path-integral formalism.