Higher spin fluctuations on spinless 4D BTZ black hole

Rodrigo Aros, Carlo Iazeolla, Per Sundell, Yihao Yin

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We construct linearized solutions to Vasiliev’s four-dimensional higher spin gravity on warped AdS3 ×ξS1 which is an Sp(2) × U(1) invariant non-rotating BTZ-like black hole with ℝ2 × T2 topology. The background can be obtained from AdS4 by means of identifications along a Killing boost K in the region where ξ2 ≡ K2 ≥ 0, or, equivalently, by gluing together two Bañados-Gomberoff-Martinez eternal black holes along their past and future space-like singularities (where ξ 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 boostK˜. 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 S1. We examine the subsector in which K anti-commutes to J and the ground state is U (1) K× U (1) -invariant of which U(1)K is broken by momenta on S1 and U (1) by quasi-normal modes. We show that a set of U (1) -invariant modes (with n units of S1 momenta) are singularity-free as master fields living on a total bundle space, although the individual Fronsdal fields have membrane-like singularities at K˜ 2= 1. We interpret our findings as an example where Vasiliev’s theory completes singular classical Lorentzian geometries into smooth higher spin geometries.

Original languageEnglish
Article number171
JournalJournal of High Energy Physics
Issue number8
Publication statusPublished - 1 Aug 2019


  • Black Holes
  • Higher Spin Gravity
  • Higher Spin Symmetry

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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