Extend Bekenstein’s theorem to Einstein–Maxwell-scalar theories with a scalar potential

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2022-07, Vol.82 (7), p.1-11, Article 654
• Main Authors: Qiu, Jianhui, Gao, Changjun
• Format: Article
• Language: English
• Subjects: Angular momentum; Astronomy; Astrophysics and Cosmology; Black holes; Conformal mapping; Coupling; Dilatons; Elementary Particles; Hadrons; Heavy Ions; Investigations; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Perturbation; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Spacetime; String Theory; Theorems; Theory of relativity
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-022-10618-0

The Bekenstein’s theorem allows us to generate an Einstein-conformal scalar solution from a single Einstein-ordinary scalar solution. In this article, we extend this theorem to the Einstein–Maxwell-scalar (EMS) theory with a non-minimal coupling between the scalar and Maxwell field when a scalar potential is also included. 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 mass, electric charge, and 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 useful 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.