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

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 $\alpha <0$ 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 $\alpha$ to obtain threshold curves numerically. We obtain threshold curves ${\alpha }_{\mathrm{th}}(a)$ of tachyonic instability for positive $\alpha$ without any $a$-bounds. We expect to find the same threshold curves ${\alpha }_{\mathrm{th}}(a)$ of tachyonic instability for negative $\alpha$ without any $a$-bound because its linearized scalar theory is invariant under the transformation of $\alpha \to -\alpha$ and $\theta \to -\theta$. In addition, it is found that the scalar mass term suppresses tachyonic instability of KN black holes.

18 pages, 4 figures, minor changes