D2 Chern-Simons gravity

We study the theory that contains two spin-2 fields. This theory can be regarded as a simplified version of higher spin gravity in AdS(3). 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 these black holes with the help of dual holographic operator product expansion. 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 AdS(3) bigravity. Moreover, the entropy of the black hole with the spin-2 hair could be reproduced from the AdS(3) bigravity in the Euclidean path-integral formalism.