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Pole structure of the Kerr Green’s function

Hayato Motohashi and Yuto Suichi

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Phys. Rev. D 114, 044022 – Published 10 August, 2026

DOI: https://doi.org/10.1103/jlrh-3jpr

Abstract

We investigate the pole structure of Kerr black-hole perturbations in the frequency domain, focusing on the building blocks of the Green’s function for the radial Teukolsky equation: the homogeneous radial solutions, the connection coefficients, and the Green’s function itself. We show that the homogeneous solutions and the local connection coefficients develop simple poles at the Matsubara frequencies, thereby establishing the Matsubara pole structure explicitly within the Teukolsky formalism for asymptotically flat Kerr black holes. At the level of the local fixed-sector connection formula, the explicit Matsubara-pole factors cancel in the ratio of connection coefficients entering a decomposed Green’s function contribution. We also identify higher-order zero-frequency singularities in the decomposed Green’s function contributions, which scale as ω−2l−1 and cancel collectively in the total radial Green’s function. These results clarify how Matsubara poles and sectoral zero-frequency singularities arise in the Teukolsky formalism and provide a frequency-domain foundation for understanding prompt response in time-domain ringdown waveforms in Kerr spacetime.

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Outline

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Phys. Rev. D 114, 044022– Published 10 August, 2026
  • Received 22 May 2026
  • Accepted 1 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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