Revisiting the analogue of the Jebsen-Birkhoff theorem in Brans-Dicke gravity

Abstract

We report the explicit form of the general static, spherically symmetric, and asymptotically flat solution of vacuum Brans-Dicke gravity in the Jordan frame, assuming that the Brans-Dicke scalar field has no singularities or zeros (except possibly for a central singularity). This general solution is conformal to the Fisher-Wyman geometry of Einstein theory and its nature depends on a scalar charge parameter. Apart from the Schwarzschild black hole, only wormhole throats and central naked singularities are possible

Discussion expanded and made more precise, credit given to previous references missed in the first version of this preprint, bibliography expanded and updated, and a slight title change. Matches version accepted in Phys. Rev. D