Higher spin fluctuations on spinless 4D BTZ black hole

Abstract

We construct linearized solutions to Vasiliev's four-dimensional higher spin gravity on warped AdS(3) x(xi)S(1) which is an Sp(2) x U(1) invariant non-rotating BTZ-like black hole with R-2 x T-2 topology. The background can be obtained from AdS(4) by means of identifications along a Killing boost K in the region where xi(2) equivalent to K-2 >= 0, or, equivalently, by gluing together two Banados-Gomberoff-Martinez eternal black holes along their past and future space-like singularities (where xi vanishes) as to create a periodic (non-Killing) time. The fluctuations are constructed from gauge functions and initial data obtained by quantizing inverted harmonic oscillators providing an oscillator realization of K and of a commuting Killing boost (K) over tilde. The resulting solution space has two main branches in which K star commutes and anti-commutes, respectively, to Vasiliev's twisted-central closed two-form J. Each branch decomposes further into two subsectors generated from ground states with zero momentum on S-1. We examine the subsector in which K anti-commutes to J and the ground state is U(1)(K) x U(1)((K) over tilde) - invariant of which U(1)(K) is broken by momenta on S-1 and U(1)((K) over tilde) by quasi-normal modes. We show that a set of U(1)((K) over tilde)-invariant modes (with n units of S-1 momenta) are singularity-free as master fields living on a total bundle space, although the individual Fronsdal fields have membrane-like singularities at (K) over tilde (2) = 1. We interpret our findings as an example where Vasiliev's theory completes singular classical Lorentzian geometries into smooth higher spin geometries.