Onset of rotating scalarized black holes in Einstein-Chern-Simons-Scalar theory

Understand

We perform the stability analysis of the Kerr black hole in the Einstein-Chern-Simons-Scalar theory with quadratic scalar coupling.

• For positive coupling parameter ($\alpha>0$), we introduce the (2+1)-dimensional hyperboloidal foliation method to show that the Kerr black hole is unstable against scalar-mode perturbation.
• In case of $\alpha<0$, it is shown that the Kerr black hole is unstable without any $\alpha$-independent bound on the rotation parameter $a$ when using the the hyperboloidal foliation method.
• The disappearance of the $a$-bound is confirmed analytically by implementing the (1+1)-dimensional linearized scalar equation.