Black holes and singularity resolution in higher spin gravity

Abstract

We investigate higher spin theories of gravity in three dimensions based on the gauge group SL(N, $\mathbb{R}$) × SL(N, $\mathbb{R}$). In these theories the usual diffeomorphism symmetry is enhanced to include higher spin gauge transformations under which traditional geometric notions of curvature and causality are no longer invariant. This implies, for example, that apparently singular geometries can be rendered smooth by a gauge transformation, much like the resolution of orbifold singularities in string theory. The classical solutions, including the recently constructed higher spin black hole, are characterized by their holonomies around the non-contractible cycles of space-time. The black hole solutions are shown to be gauge equivalent to a BTZ black hole which is charged under a set of U(1) Chern- Simons fields. Nevertheless, depending on the choice of embedding of the gravitational gauge group, the space-time geometry may be non-trivial. We study in detail the N = 3 example, where this observation allows us to find a gauge where the black hole geometry takes a simple form and the thermodynamic properties can be studied.