A geometric framework for black hole perturbations

TL;DR

This paper introduces a geometric framework for black hole perturbations that uses time surfaces connecting the future event horizon and null infinity, improving the analysis of quasinormal modes and perturbation potentials.

Contribution

It proposes a new geometric approach to black hole perturbation theory that addresses limitations of traditional time surfaces and enhances the representation of eigenfunctions and potentials.

Findings

Resolves issues with quasinormal mode eigenfunction representation.

Constructs short-ranged potentials in frequency domain.

Provides a more physically relevant framework for black hole perturbations.

Abstract

Black hole perturbation theory is typically studied on time surfaces that extend between the bifurcation sphere and spatial infinity. From a physical point of view, however, it may be favorable to employ time surfaces that extend between the future event horizon and future null infinity. This framework resolves problems regarding the representation of quasinormal mode eigenfunctions and the construction of short-ranged potentials for the perturbation equations in frequency domain.