Beyond quasinormal modes: a complete mode decomposition of black hole perturbations

Arnaudo, Paolo, Carballo, Javier and Withers, Benjamin (2025) Beyond quasinormal modes: a complete mode decomposition of black hole perturbations. arXiv. (doi:10.48550/arXiv.2510.18956).

Record type: Article

Abstract

We show that retarded Green's functions of black hole spacetimes can be expressed as a convergent mode sum everywhere in spacetime. At late times a quasinormal mode sum converges, while at early times a Matsubara (or, Euclidean) mode sum converges. The two regions are separated by a lightcone which scatters from the black hole potential. The Matsubara sum is a Fourier series on the Euclidean thermal circle associated to the early time region. We illustrate our results for Pöschl-Teller, BTZ, and Schwarzschild. In the case of Schwarzschild, we express the branch cut contribution as a convergent sum of de Sitter quasinormal modes as , and exploit recent exact solutions to the Heun connection problem. In each case we analytically show convergence by studying the asymptotics of residue sums and also provide numerical demonstrations.

This record has no associated files available for download.