Horizon instability of the extremal BTZ black hole

Samuel E. Gralla, Arun Ravishankar, Peter Zimmerman

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study real-time propagation of a massive scalar field on the extremal BTZ black hole spacetime, focusing on the Aretakis instability of the event horizon. We obtain a simple time-domain expression for the AdS3 retarded Green function with Dirichlet boundary conditions and construct the corresponding time-domain BTZ retarded Green function using the method of images. The field decays at different rates on and off the horizon, indicating that transverse derivatives grow with time on the horizon (Aretakis instability). We solve the null geodesic equation in full generality and show that the instability is associated with a class of null geodesics that orbit near the event horizon arbitrarily many times before falling in. In an appendix we also treat the problem in the frequency domain, finding consistency between the methods.

Original languageEnglish (US)
Article number94
JournalJournal of High Energy Physics
Issue number5
StatePublished - May 1 2020


  • AdS-CFT
  • Black Holes
  • Black Holes in String Theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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