Gravity with a generalized conformal scalar field: Theory and solutions

We naturally extend general relativity 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.

Automated summary

This theory extends general relativity through conformal coupling with a scalar field, incorporating a scalar-Gauss-Bonnet sector and featuring second-order equations of motion belonging to the Horndeski class. The theory includes a purely geometrical field equation, allowing for easy identification of closed-form black hole solutions and cosmologies without the need for approximations or numerical methods.