A global definition of quasinormal modes for Kerr-AdS Black Holes

TL;DR

This paper defines quasinormal modes for Kerr-AdS black holes using boundary conditions at infinity, showing their frequencies form a discrete set with finite-rank poles, applicable to various boundary conditions and black hole rotations.

Contribution

It provides a rigorous, boundary-condition-independent framework for defining quasinormal modes of Kerr-AdS black holes.

Findings

Quasinormal frequencies are discrete complex numbers.

Poles are of finite rank.

Applicable to broad boundary conditions and any black hole rotation.

Abstract

The quasinormal frequencies of massive scalar fields on Kerr-AdS black holes are identified with poles of a certain meromorphic family of operators, once boundary conditions are specified at the conformal boundary. Consequently, the quasinormal frequencies form a discrete subset of the complex plane and the corresponding poles are of finite rank. This result holds for a broad class of elliptic boundary conditions, with no restrictions on the rotation speed of the black hole.