A Selberg zeta function for warped AdS3 black holes

Victoria L. Martin, Rahul Poddar*, Agla Þórarinsdóttir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The Selberg zeta function and trace formula are powerful tools used to calculate kinetic operator spectra and quasinormal modes on hyperbolic quotient spacetimes. In this article, we extend this formalism to non-hyperbolic quotients by constructing a Selberg zeta function for warped AdS3 black holes. We also consider the so-called self-dual solutions, which are of interest in connection to near-horizon extremal Kerr. We establish a map between the zeta function zeroes and the quasinormal modes on warped AdS3 black hole backgrounds. In the process, we use a method involving conformal coordinates and the symmetry structure of the scalar Laplacian to construct a warped version of the hyperbolic half-space metric, which to our knowledge is new and may have interesting applications of its own, which we describe. We end by discussing several future directions for this work, such as computing 1-loop determinants (which govern quantum corrections) on the quotient spacetimes we consider, as well as adapting the formalism presented here to more generic orbifolds.

Original languageEnglish
Article number49
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 11 Jan 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).

Other keywords

  • Black Holes
  • Differential and Algebraic Geometry
  • Space-Time Symmetries


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