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

TL;DR

This paper derives the general static, spherically symmetric vacuum solutions in Brans-Dicke gravity, revealing their relation to Einstein solutions and classifying possible geometries including black holes, wormholes, and singularities.

Contribution

It provides the explicit form of the general solution in Brans-Dicke theory and clarifies its relation to Einstein gravity solutions, extending the understanding of scalar-tensor gravity.

Findings

Solutions include black holes, wormholes, and naked singularities.

The solutions are conformal to Fisher-Wyman geometries.

The nature of solutions depends on the scalar charge parameter.

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