Spacetime Geometry in Higher Spin Gravity

TL;DR

This paper demonstrates that higher spin gauge transformations can alter the perceived causal structure of solutions in higher spin gravity, transforming wormhole-like solutions into black holes with horizons, revealing gauge-dependent notions of spacetime features.

Contribution

The authors explicitly show that higher spin gauge transformations can convert wormhole solutions into black holes with horizons in SL(3,R) higher spin gravity, highlighting gauge-dependent spacetime properties.

Findings

Solutions can be gauge-transformed into black holes with horizons

Existence of two distinct AdS_3 vacua connected by RG flow

Finite temperature solutions exhibit these gauge-dependent features

Abstract

Higher spin gravity is an interesting toy model of stringy geometry. Particularly intriguing is the presence of higher spin gauge transformations that redefine notions of invariance in gravity: the existence of event horizons and singularities in the metric become gauge dependent. In previous work, solutions of spin-3 gravity in the SL(3,R) x SL(3,R) Chern-Simons formulation were found, and were proposed to play the role of black holes. However, in the gauge employed there, the spacetime metric describes a traversable wormhole connecting two asymptotic regions, rather than a black hole. In this paper, we show explicitly that under a higher spin gauge transformation these solutions can be transformed to describe black holes with manifestly smooth event horizons, thereby changing the spacetime causal structure. A related aspect is that the Chern-Simons theory admits two distinct AdS_3 vacua with different asymptotic W-algebra symmetries and central charges. We show that these vacua are connected by an explicit, Lorentz symmetry-breaking RG flow, of which our solutions represent finite temperature generalizations. These features will be present in any SL(N,R) x SL(N,R) Chern-Simons theory of higher spins.