Unfolding, higher spins, metaplectic groups and resolution of classical singularities

Abstract

We review and extend some recent results concerning the analysis of spacetime singularities in four-dimensional higher spin gravity, summarizing how the coupling of the gravitational field to massless higher spins may provide resolution mechanisms. We elucidate such mechanisms at the level of curvature singularities and degenerate metrics in exact as well as linearized solutions to Vasiliev's equations. As a preamble, we review the underlying higher-spin algebra and its metaplectic group extensions, after which we detail various gauge functions encoding the $AdS_4$ vacuum and the non-rotating Banados--Gomberoff--Martinez (BGM) metric, the four-dimensional lift of the spinless BTZ black hole, in different coordinate patches related by transition functions. We then revisit how, within the unfolded formalism, it is natural extend the BGM black hole through its causal singularity. Finally, we compare the metric-like and unfolded descriptions of scalar fluctuations over the (extended) BGM background, showing how the latter description maps singularities to well-defined metaplectic group elements providing regular values for the Weyl zero-form master field, which thus admits continuation over the full extended BGM spacetime.