Black hole determinants and quasinormal modes

TL;DR

This paper presents a new method to compute functional determinants in thermal spacetimes using quasinormal modes, facilitating analysis of quantum effects in black hole and cosmological backgrounds within holography.

Contribution

It introduces a formula expressing functional determinants as a product over quasinormal modes, enabling efficient calculations in various thermal spacetimes.

Findings

Efficient computation of scalar determinants in thermal AdS, BTZ black hole, and de Sitter spaces.

Highlights the conceptual utility for analyzing 1/N corrections in holographic duals.

Provides a practical tool for quantum field theory in curved spacetimes.

Abstract

We derive an expression for functional determinants in thermal spacetimes as a product over the corresponding quasinormal modes. As simple applications we give efficient computations of scalar determinants in thermal AdS, BTZ black hole and de Sitter spacetimes. We emphasize the conceptual utility of our formula for discussing `1/N' corrections to strongly coupled field theories via the holographic correspondence.