Paper detail

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

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