Slowly rotating black holes in the novel Einstein–Maxwell-scalar theory

We investigate a slowly rotating black hole solution in a novel Einstein–Maxwell-scalar theory, which is prompted by the classification of general Einstein–Maxwell-scalar theory. The gyromagnetic ratio of this black hole is calculated, and it increases as the second free parameter β increases, but decreases with the increasing parameter γ ≡ 2 α 2 1 + α 2 . In the Einstein–Maxwell-dilaton (EMD) theory, the parameter β vanishes but the free parameter α governing the strength of the coupling between the dilaton and the Maxwell field remains. The gyromagnetic ratio is always less than 2, the well-known value for a Kerr–Newman (KN) black hole as well as for a Dirac electron. Scalar hairs reduce the magnetic dipole moment in dilaton theory, resulting in a drop in the gyromagnetic ratio. However, we find that the gyromagnetic ratio of two can be realized in this Einstein–Maxwell-scalar theory by increasing β and the charge-to-mass ratio Q / M simultaneously (recall that the gyromagnetic ratio of KN black holes is independent of Q / M ). The same situation also applies to the angular velocity of a locally non-rotating observer. Moreover, we analyze the period correction for circular orbits in terms of charge-to-mass ratio, as well as the correction of the radius of the innermost stable circular orbits. It is found the correction increases with β but decreases with Q / M . Finally, the total radiative efficiency is investigated, and it can vanish once the effect of rotation is considered.