Symmetry of Brans-Dicke gravity as a novel solution-generating technique

A symmetry of Brans-Dicke gravity in (electro-)vacuo or in the presence of conformally invariant matter is presented and used as a solution-generating technique starting from a known solution as a seed. This novel technique is applied to generate, as examples, new spatially homogeneous and isotropic cosmologies, a 3-parameter family of spherical time-dependent spacetimes conformal to a Campanelli-Lousto geometry, and a family of cylindrically symmetric geometries.