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

TL;DR

This paper introduces a new symmetry in Brans-Dicke gravity that acts as a solution-generating tool, enabling the creation of diverse new spacetime solutions from known ones in various symmetric contexts.

Contribution

The paper presents a novel symmetry-based method for generating solutions in Brans-Dicke gravity, expanding the toolkit for exploring its solution space.

Findings

Generated new cosmological solutions with spatial homogeneity and isotropy.

Constructed a family of spherical, time-dependent spacetimes conformal to known geometries.

Developed cylindrically symmetric geometries using the symmetry technique.

Abstract

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.