Connecting quasinormal modes and heat kernels in 1-loop determinants

Abstract

We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.

22 pages

References in corpus (6)

• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Ruelle zeta function at zero for surfaces
• Tweaking one-loop determinants in AdS${}_3$
• Power spectrum of the geodesic flow on hyperbolic manifolds
• Holographic formula for the determinant of the scattering operator in thermal AdS

Cited by in corpus (10)

• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• BTZ one-loop determinants via the Selberg zeta function for general spin
• Normal modes in thermal AdS via the Selberg zeta function
• Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
• A Selberg zeta function for warped AdS${}_3$ black holes
• Long Strings and Quasinormal Winding Modes
• Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity
• De Sitter Horizon Edge Partition Functions
• Black hole one-loop determinants in the large dimension limit
• Rényi entropy of single-character CFTs on the torus