QNM orthogonality relations for AdS black holes

TL;DR

This paper develops orthogonality relations for quasinormal modes of asymptotically AdS black holes, linking complex radial contours, CPT symmetry, and holography to advance understanding of black hole perturbations.

Contribution

It introduces a novel orthogonality framework for AdS black hole quasinormal modes using a CPT-modified product on a complex contour, inspired by de Sitter and Kerr analyses.

Findings

Orthogonality relations for AdS black hole modes established.

Connection between radial contour and dual QFT on Schwinger-Keldysh contour.

Framework applicable to real-time holography and wormhole geometries.

Abstract

We present orthogonality relations for quasinormal modes of a wide class of asymptotically AdS black holes. The definition is obtained from a standard product, modified by a CPT operator and placed on a complex radial contour which avoids branch points of the modes. They are inspired by existing constructions for de Sitter and Kerr spacetimes. The CPT operator is needed to map right eigenfunctions of the Hamiltonian into left eigenfunctions. The radial contour connects two copies of the dual QFT on a thermal Schwinger-Keldysh contour, making contact with real-time holography and the double cone wormhole.