Year: 2026
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 $Λ\to 0^+$, 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.
DOI: 10.1103/1bcl-q79x
Institution: University of Southampton
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164353361