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

We make the research on a slowly rotating black hole solution in a new Einstein-Maxwell-scalar theory, which is an extension of the Einstein-Maxwell-dilaton theory. The gyromagnetic ratio of this black hole is calculated and it increases with the parameter $\beta$, but decreases with the parameter $\gamma$. In the Einstein-Maxwell-dilaton theory where the parameter $\beta$ is in the absence, the gyromagnetic ratio is always less than $2$, the gyromagnetic ratio for Kerr-Newman black hole. Now we find that the standard gyromagnetic ratio $2$ can also be realized in this Einstein-Maxwell-scalar theory by increasing $\beta$ and $\gamma$ simultaneously. The same value of angular velocity of locally non-rotating observer as that in Kerr-Newman black hole can also be obtained in the same way. We also investigated the correction of period for circular orbits with respect to charge to mass ratio and the correction of radius of innermost stable circular orbits. We find that the correction becomes smaller and smaller with the increase of $\beta$. It is also shown that the radiative efficiency in the thin accretion disk model, for small value of $\beta$ and large value of charge to mass ratio, the efficiency vanishes due to lacking of the enough stress and dynamic friction in the accretion model. A phantom Maxwell black hole is investigated in this theory as an example of exact slowly rotating black hole solution. Therefore, formula for angular velocity of the event horizon is shown. Correction of the radius of innermost stable circular orbits and of radiative efficiency are investigated subsequently. It is found that the correction up to first order of the perturbation parameter can vanish for some value of charge-to-mass ratio. The total radiative efficiency can also vanish once the effect of rotation is considered.Comment: 27 figure