Scalarization of Kerr–Newman black holes in the Einstein–Chern–Simons-scalar theory

Kun-Hui Fan; Yun Soo Myung; De-Cheng Zou; Meng-Yun Lai

doi:10.1140/epjc/s10052-024-13030-y

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 679
https://doi.org/10.1140/epjc/s10052-024-13030-y

Regular Article - Theoretical Physics

Scalarization of Kerr–Newman black holes in the Einstein–Chern–Simons-scalar theory

Kun-Hui Fan¹, Yun Soo Myung², De-Cheng Zou¹^,3 and Meng-Yun Lai¹^d

¹ College of Physics and Communication Electronics, Jiangxi Normal University, 330022, Nanchang, China
² Institute of Basic Sciences and Department of Computer Simulation, Inje University, 50834, Gimhae, Korea
³ Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, China

^d mengyunlai@jxnu.edu.cn

Received: 10 January 2024
Accepted: 14 June 2024
Published online: 9 July 2024

Abstract

We investigate the tachyonic instability of Kerr–Newman (KN) black hole with a rotation parameter a in the Einstein–Chern–Simons-scalar theory coupled with a quadratic massive scalar field. This instability analysis corresponds to exploring the onset of spontaneous scalarization for KN black holes. First, we find no a-bound for $α < 0$ $\alpha <0$ case by considering (1 + 1)-dimensional analytical method. A direct numerical method is adopted to explore (2 + 1)-dimensional time evolution of a massive scalar perturbation with positive and negative $α$ $\alpha$ to obtain threshold curves numerically. We obtain threshold curves $α_{th} (a)$ $\alpha _{\textrm{th}}(a)$ of tachyonic instability for positive $α$ $\alpha$ without any a-bounds. We expect to find the same threshold curves $α_{th} (a)$ $\alpha _{\textrm{th}}(a)$ of tachyonic instability for negative $α$ $\alpha$ without any a-bound because its linearized scalar theory is invariant under the transformation of $α \to - α$ $\alpha \rightarrow -\alpha$ and $θ \to - θ .$ $\theta \rightarrow -\theta .$ In addition, it is found that the scalar mass term suppresses tachyonic instability of KN black holes, while the black hole charge promotes the instability (disregarding the contribution of the charge to the existence conditions $M^{2} - Q^{2} \geq a^{2})$ $M^2-Q^2\ge a^2)$ .

© The Author(s) 2024

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