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 possibleComment: 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.