Gravity with a generalized conformal scalar field: Theory and solutions

TL;DR

This paper extends gravity theories with a conformally invariant scalar field, resulting in a class of models with second-order equations that admit exact black hole and cosmological solutions, facilitating studies of scalar-Gauss-Bonnet effects.

Contribution

It introduces a generalized conformal scalar field extension of gravity with second-order equations, enabling explicit solutions without approximations.

Findings

Derived exact black hole solutions.

Obtained cosmological solutions within the extended theory.

Connected the model to 4D Einstein-Gauss-Bonnet gravity.

Abstract

We naturally extend the theory of gravity with a conformally coupled scalar field by only requiring conformal invariance of the scalar field equation of motion and not of the action. The classically extended theory incorporates a scalar-Gauss-Bonnet sector and has second-order equations of motion, belonging to the Horndeski class. Remarkably, the theory features a purely geometrical field equation that allows for closed-form black hole solutions and cosmologies to be easily found. These solutions permit investigations of in-vogue scalar-Gauss-Bonnet corrections to the gravitational action without the need of resorting to approximations or numerical methods. We discuss on the connection to the recently formulated 4D Einstein-Gauss-Bonnet theory of gravity.