https://doi.org/10.1140/epjc/s10052-025-15096-8
Regular Article - Theoretical Physics
Non-linearly scalarized supermassive black holes
1
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, China
2
School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, Shandong, China
3
Department of Physics and Siyuan Laboratory, Jinan University, 510632, Guangzhou, China
a
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Received:
23
September
2025
Accepted:
18
November
2025
Published online:
1
December
2025
Abstract
In this study, we investigate a nonlinear mechanism driving the formation of scalarized rotating black holes within a scalar-Gauss–Bonnet gravity framework that includes an additional squared Gauss–Bonnet term. With the specific coupling function, Kerr metric is a solution to this modified gravity. In linear level Kerr black holes are stable against the scalar perturbation, while nonlinearly they suffer the so-called “nonlinear scalarization” and are unstable. By employing a pseudo-spectral method, we derive the spectrum of nonlinearly scalarized rotating black hole solutions, revealing multiple scalarized branches. Our analysis demonstrates that both the black hole’s spin and the additional squared Gauss–Bonnet term significantly influence the existence and properties of these solutions. Furthermore, we explore the thermodynamic properties of nonlinearly scalarized rotating black holes, and find that the scalarized black holes are entropically favored over Kerr black holes of the same mass and spin across a wide range of parameters.
© The Author(s) 2025
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