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

TL;DR

This paper extends Bekenstein's theorem to Einstein-Maxwell-scalar theory with non-minimal coupling, enabling the generation of new black hole solutions and analyzing their physical properties, with potential applications in black hole perturbations and scalarization.

Contribution

The paper introduces an extension of Bekenstein's theorem to Einstein-Maxwell-conformal-scalar theory, allowing for the construction of new solutions and analysis of their invariance properties.

Findings

New conformal dilaton black hole solutions found.

Conformal invariance of mass, charge, and angular momentum established.

The extended theorem may aid in black hole perturbation studies.

Abstract

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