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

Fuente: arXiv
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Hauptverfasser: Arnaudo, Paolo, Carballo, Javier, Withers, Benjamin
Format: Preprint
Veröffentlicht: 2025
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author Arnaudo, Paolo
Carballo, Javier
Withers, Benjamin
author_facet Arnaudo, Paolo
Carballo, Javier
Withers, Benjamin
contents 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 $Λ\to 0^+$, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_18956
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Beyond quasinormal modes: a complete mode decomposition of black hole perturbations
Arnaudo, Paolo
Carballo, Javier
Withers, Benjamin
General Relativity and Quantum Cosmology
High Energy Physics - Theory
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 $Λ\to 0^+$, 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.
title Beyond quasinormal modes: a complete mode decomposition of black hole perturbations
topic General Relativity and Quantum Cosmology
High Energy Physics - Theory
url https://arxiv.org/abs/2510.18956