Spin-charge induced spontaneous scalarization of Kerr-Newman black holes

We investigate the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell -scalar (EMS) theory with a positive coupling parameter alpha. This corresponds to exploring the onset of spontaneous scalarization for KN black holes. For this purpose, we use the hyperboloidal foliation method to solve the linearized scalar equation numerically. We obtain a 3D graph [log10 alpha(a; Q)] which indicates the onset surface for spontaneous scalarization of KN black holes in the EMS theory. We find that there is no lower bound on the rotational parameter a, but its upper bound is given by M2 - Q2 >= a2. Also, we confirm that the high rotation enhances spontaneous scalarization of KN black holes in the EMS theory.