When the Ringing Stops: Purely Imaginary Modes in the Ringdown Spectrum of Dynamical Black Holes
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| Format: | Preprint |
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2026
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| author | Capuano, Lodovico Lovo, Thomas Prieto-Varela, Gorka Sarkar, Subhodeep Kuntz, Adrien Barausse, Enrico Kothawala, Dawood |
| author_facet | Capuano, Lodovico Lovo, Thomas Prieto-Varela, Gorka Sarkar, Subhodeep Kuntz, Adrien Barausse, Enrico Kothawala, Dawood |
| contents | We extend the frequency-domain analysis of quasinormal modes in a dynamical, spherically symmetric black hole spacetime undergoing constant-rate mass evolution. In particular, we report a novel feature of the spectrum: the presence of purely imaginary eigenvalues in addition to the usual light-ring modes. We study the frequencies of these modes both analytically and numerically. The analytical calculation uses a novel formalism based on recent advances in connection coefficients of Heun functions. We then compute the frequencies numerically using a spectral method on hyperboloidal slices and find excellent agreement between the two approaches. Finally, we validate the frequency-domain results against an independent set of time-domain simulations. Our analysis shows that the purely imaginary modes govern the late-time signal through exponentially decaying tails. In the Schwarzschild limit, both frequency- and time-domain studies consistently show that the purely imaginary modes give rise to the familiar Schwarzschild power-law tail. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_28951 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | When the Ringing Stops: Purely Imaginary Modes in the Ringdown Spectrum of Dynamical Black Holes Capuano, Lodovico Lovo, Thomas Prieto-Varela, Gorka Sarkar, Subhodeep Kuntz, Adrien Barausse, Enrico Kothawala, Dawood General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory We extend the frequency-domain analysis of quasinormal modes in a dynamical, spherically symmetric black hole spacetime undergoing constant-rate mass evolution. In particular, we report a novel feature of the spectrum: the presence of purely imaginary eigenvalues in addition to the usual light-ring modes. We study the frequencies of these modes both analytically and numerically. The analytical calculation uses a novel formalism based on recent advances in connection coefficients of Heun functions. We then compute the frequencies numerically using a spectral method on hyperboloidal slices and find excellent agreement between the two approaches. Finally, we validate the frequency-domain results against an independent set of time-domain simulations. Our analysis shows that the purely imaginary modes govern the late-time signal through exponentially decaying tails. In the Schwarzschild limit, both frequency- and time-domain studies consistently show that the purely imaginary modes give rise to the familiar Schwarzschild power-law tail. |
| title | When the Ringing Stops: Purely Imaginary Modes in the Ringdown Spectrum of Dynamical Black Holes |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.28951 |