Quasi-normal modes of slowly-rotating Johannsen black holes

Yuhao Guo; Swarnim Shashank; Cosimo Bambi

doi:10.1140/epjc/s10052-025-14118-9

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 425
https://doi.org/10.1140/epjc/s10052-025-14118-9

Regular Article - Theoretical Physics

Quasi-normal modes of slowly-rotating Johannsen black holes

Yuhao Guo¹, Swarnim Shashank¹ and Cosimo Bambi¹^,2^a

¹ Center for Astronomy and Astrophysics, Center for Field Theory and Particle Physics, and Department of Physics, Fudan University, 200438, Shanghai, China
² School of Natural Sciences and Humanities, New Uzbekistan University, 100007, Tashkent, Uzbekistan

^a bambi@fudan.edu.cn

Received: 5 January 2025
Accepted: 23 March 2025
Published online: 16 April 2025

Abstract

The detection of gravitational waves with ground-based laser interferometers has opened a new window to test and constrain General Relativity (GR) in the strong, dynamical, and non-linear regime. In this paper, we follow an agnostic approach and we study the quasi-normal modes of gravitational perturbations of Johannsen black holes under the assumptions of the validity of the Einstein Equations and of low values of the black hole spin parameter and deformation parameters. We find that the deformation parameter $α_{13}$ $\alpha _{13}$ has a stronger impact on the quasi-normal modes than the other leading order deformation parameters ( $α_{22}$ $\alpha _{22}$ , $α_{52}$ $\alpha _{52}$ , and $ϵ_{3}$ $\epsilon _{3}$ ). We derive a fitting formula for the fundamental modes with $l = 2$ $$l=2$$ and $l = 3$ $$l=3$$ for the deformation parameter $α_{13}$ $\alpha _{13}$ valid in the slow rotation approximation ( $a_{*} < 0.4$ $$a_* < 0.4$$ ). Finally, we constrain $α_{13}$ $\alpha _{13}$ from the event GW170104; within our analysis, we find that the data of GW170104 are consistent with the predictions of GR.

© The Author(s) 2025

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