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We construct linearized solutions to Vasiliev's four-dimensional higher spingravity on warped $AdS_3 \times_\xi S^1$ which is an $Sp(2)\times U(1)$invariant non-rotating BTZ-like black hole with $\mathbb{R}^2\times T^2$topology. The background can be obtained from $AdS_4$ by means ofidentifications along a Killing boost $K$ in the region where $\xi^2\equivK^2\geqslant 0$, or, equivalently, by gluing together twoBa\~nados--Gomberoff--Martinez eternal black holes along their past and futurespace-like singularities (where $\xi$ vanishes) as to create a periodic(non-Killing) time. The fluctuations are constructed from gauge functions andinitial data obtained by quantizing inverted harmonic oscillators providing anoscillator realization of $K$ and of a commuting Killing boost $\widetilde K$.The resulting solution space has two main branches in which $K$ star commutesand anti-commutes, respectively, to Vasiliev's twisted-central closed two-form$J$. Each branch decomposes further into two subsectors generated from groundstates with zero momentum on $S^1$. We examine the subsector in which $K$anti-commutes to $J$ and the ground state is $U(1)_K\times U(1)_{\widetildeK}$-invariant of which $U(1)_K$ is broken by momenta on $S^1$ and$U(1)_{\widetilde K}$ by quasi-normal modes. We show that a set of$U(1)_{\widetilde K}$-invariant modes (with $n$ units of $S^1$ momenta) aresingularity-free as master fields living on a total bundle space, although theindividual Fronsdal fields have membrane-like singularities at $\widetildeK^2=1$. We interpret our findings as an example where Vasiliev's theorycompletes singular classical Lorentzian geometries into smooth higher spingeometries.

Higher spin fluctuations on spinless 4D BTZ black hole