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Odd-parity ringdown gravitational waves of a spherically symmetric black hole with perfect fluid accretion

Rikuto Ohashi1,*, Yasutaka Koga2, Hiroyuki Nakano3, Kota Ogasawara4, and Chul-Moon Yoo1,5

  • *Contact author: ohashi.rikuto.z3@s.mail.nagoya-u.ac.jp
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Phys. Rev. D 114, 104003 – Published 2 November, 2026

DOI: https://doi.org/10.1103/bt5p-xfz2

Abstract

The ringdown waves from a black hole offer a clean probe of strong-field gravity, but a matter distribution that may be present around a realistic black hole renders the background spacetime dynamical and the ringdown frequencies time dependent. We study the odd-parity ringdown of a Schwarzschild black hole that grows through the dilute, steady, spherically symmetric accretion of a perfect fluid. Working to first order in the accretion rate, we compute the ringdown waveform directly in the time domain on this dynamical background. Since the odd-parity matter perturbation decouples from the metric perturbation, the wave mode can be described by a purely tensorial mode on the accreting background. In particular, the ratio of the imaginary to the real part of the frequency cancels both the secular variation caused by the growth of the black hole and the redshift factor, so that its deviation from the Schwarzschild value purely reflects the surrounding environment. The time dependence of the frequency, on the other hand, reflects the accretion rate and allows us to define a second observable tied to it. We argue that measuring these observables across multiple modes may provide significant information to constrain the surrounding environment of the black hole.

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Phys. Rev. D 114, 104003– Published 2 November, 2026
  • Received 17 July 2026
  • Accepted 29 September 2026
Article part of CHORUS
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