Slowly rotating black holes in the 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 theories. The gyromagnetic ratio of this black hole is calculated, and it increases as the second free parameter $\beta$ increases, but decreases with the increasing parameter $\gamma\equiv \frac{2 \alpha^{2}}{1+\alpha^2}$. In the Einstein-Maxwell-dilaton (EMD) theory, the parameter $\beta$ vanishes, but the free parameter $\alpha$ 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 $\beta$ 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 $\beta$ but decreases with $Q/M$. Finally, the total radiative efficiency is investigated, and it can vanish once the effect of rotation is considered.