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The Bekenstein's theorem allows us to generate a Einstein-conformal scalarsolution from a single Einstein-ordinary scalar solution. In this article, weextend this theorem to Einstein-Maxwell-scalar (EMS) theory with a non-minimalcoupling between the scalar and Maxwell field. As applications of this extendedtheorem, the well-known static dilaton solution and rotating solution with aspecific coupling between dilaton and Maxwell field are considered, and newconformal dilaton black hole solutions are found. The Noether charges such asthe mass, electric charge, angular momentum are compared between the old andnew black hole solutions connected by conformal transformations, and they arefound conformally invariant. We speculate that the theorem may be helpful inthe computations of metric perturbations and spontaneous scalarization of blackholes in the Einstein-Maxwell-conformal-scalar theory since they can be mappedto the corresponding EMS theories, which have been investigated in detail.

Extending Bekenstein's theorem in order to search exact solutions of Einstein-Maxwell-conformal-scalar equations