Original title: Excitation factors and exceptional points of Kerr-de Sitter quasinormal modes
Dario Rossi, Naritaka Oshita, Leonardo Gualtieri, Emanuele Berti · September 2026
When black holes are disturbed, they ring like bells. These ringing vibrations are called quasinormal modesThe characteristic vibration frequencies of a black hole when it is perturbed, which decay over time., and each mode has an excitation factor that measures how strongly it gets triggered. In this paper, researchers studied spinning black holes in an expanding universe, known as Kerr-de SitterA rotating black hole in a universe with dark energy, described by the Kerr-de Sitter metric. black holes. They calculated these excitation factorsA measure of how strongly each vibration mode is triggered or excited by a disturbance. using two mathematical techniques. They found that these black holes regularly have "exceptional pointsPoints in the spectrum where two different vibration modes have the same complex frequency and merge.," which are special spots where the vibration frequencies of different overtones match up exactly. Near these points, the ringing modes show a hysteresis effect. The excitation strength of each individual mode jumps dramatically, and the modes shift to nearly opposite phases. Finally, testing their results against simpler spinning black holes showed good agreement.
Imagine two guitar strings tuned to the same note and played together; they reinforce each other and become louder. Normally, strings have distinct pitches, but here they match perfectly. In this paper, black hole vibrations can have the same frequency at exceptional points, and near these points, their strength changes depending on the approach, like the strings reinforcing and their phases splitting.
This work helps understand how black holes vibrate in a universe with dark energy, which could affect gravitational wave observations. It reveals new behaviors in the spectra of rotating black holes that connect to simpler cases.
The abstract does not discuss how these theoretical results could be tested observationally or what physical mechanisms cause the hysteresis phenomenon. The study is purely computational and does not extend to experimental validation or broader implications.
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Excitation factors and exceptional points of Kerr-de Sitter quasinormal modes — Dario Rossi, Naritaka Oshita, Leonardo Gualtieri et al.
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.