Black Holes and Singularity Resolution in Higher Spin Gravity

TL;DR

This paper explores higher spin gravity theories in three dimensions, demonstrating how gauge transformations can resolve singularities and analyzing black hole solutions through their gauge equivalences and thermodynamics.

Contribution

It introduces a gauge-theoretic approach to higher spin black holes, showing how singularities can be gauge artifacts and providing detailed analysis for the N=3 case.

Findings

Higher spin gauge transformations can smooth out singular geometries.

Black holes in higher spin gravity are gauge equivalent to BTZ black holes.

Thermodynamic properties of higher spin black holes are characterized.

Abstract

We investigate higher spin theories of gravity in three dimensions based on the gauge group SL(N,R)*SL(N,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.