A Selberg zeta function for warped AdS${}_3$ black holes

Abstract

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 AdS${}_3$ 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 AdS${}_3$ 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.

arXiv comment23 pages, minor revisions and corrections of typos

References in corpus (38)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• The Kerr/CFT Correspondence
• The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2
• Warped AdS_3 Black Holes
• Hidden Conformal Symmetry of the Kerr Black Hole
• Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section
• One-loop Partition Functions of 3D Gravity
• Choptuik Scaling and Quasinormal Modes in the AdS/CFT Correspondence
• Warped Conformal Field Theory as Lower Spin Gravity
• Black hole determinants and quasinormal modes
• The Heat Kernel on AdS_3 and its Applications
• Anti-de Sitter space, squashed and stretched
• Quasi-normal modes of warped black holes and warped AdS/CFT correspondence
• Stability of warped AdS3 vacua of topologically massive gravity
• Hopfing and Puffing Warped Anti-de Sitter Space
• Tweaking one-loop determinants in AdS${}_3$
• Sailing from Warped AdS_3 to Warped dS_3 in Topologically Massive Gravity
• Selberg trace formula in hyperbolic band theory
• Quantum Correction to the Entropy of the (2+1)-Dimensional Black Hole
• Hidden Conformal Symmetry of Self-Dual Warped AdS_3 Black Holes in Topological Massive Gravity
• Ray-Singer Torsion for a Hyperbolic 3-Manifold and Asymptotics of Chern-Simons-Witten Invariant
• Self-Dual Warped AdS${}_3$ Black Holes
• Warped Black Holes in Lower-Spin Gravity
• From accelerating and Poincaré coordinates to black holes in spacelike warped AdS${}_3$, and back
• Hidden Conformal Symmetry of Warped AdS_3 Black Holes
• Quasinormal Modes of Self-Dual Warped AdS${}_3$ Black Hole in Topological Massive Gravity
• Central Charges for AdS Black Holes
• Connecting quasinormal modes and heat kernels in 1-loop determinants
• BTZ one-loop determinants via the Selberg zeta function for general spin
• Heat-Kernel Asymptotics of Locally Symmetric Spaces of Rank One and Chern-Simons Invariants
• Functional determinants, generalized BTZ geometries and Selberg zeta function
• Stability of warped AdS3 black holes in Topologically Massive Gravity under scalar perturbations
• Truncated Heat Kernel and One-Loop Determinants for the BTZ Geometry
• Quantum Corrections to Bekenstein-Hawking Black Hole Entropy and Gravity Partition Functions
• Analytic Torsion on Hyperbolic Manifolds and the Semiclassical Approximation for Chern-Simons Theory
• Computing black hole partition functions from quasinormal modes
• Seiberg-Witten prepotential from WZNW conformal block: Langlands duality and Selberg trace formula

Cited by in corpus (1)

• Love symmetry in higher-dimensional rotating black hole spacetimes