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

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 (α>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 α<0, it is shown that the Kerr black hole is unstable without any α-independent bound on the rotation parameter a when using the hyperboloidal foliation method. The disappearance of the a-bound is confirmed analytically by implementing the (1+1)-dimensional linearized scalar equation.