Spherical Structures in Conformal Gravity and its Scalar-Tensor Extension

TL;DR

This paper explores spherically symmetric solutions in Conformal Gravity and its scalar-tensor extension, revealing diverse structures including finite mass solutions, linear potentials, and gravitational solitons, enhancing understanding of these alternative gravitational theories.

Contribution

It provides new solutions and insights into the structure of spherically symmetric configurations in Conformal Gravity and its scalar-tensor extension, including finite mass and soliton solutions.

Findings

Finite mass solutions with linear potential in pure Conformal Gravity.

Rich solution structures in scalar-tensor extension, including finite and open solutions.

Existence of gravitational solitons in the scalar-tensor theory.

Abstract

We study spherically-symmetric structures in Conformal Gravity and in a scalar-tensor extension and gain some more insight about these gravitational theories. In both cases we analyze solutions in two systems: perfect fluid solutions and boson stars of a self-interacting complex scalar field. In the purely tensorial (original) theory we find in a certain domain of parameter space finite mass solutions with a linear gravitational potential but without a Newtonian contribution. The scalar-tensor theory exhibits a very rich structure of solutions whose main properties are discussed. Among them, solutions with a finite radial extension, open solutions with a linear potential and logarithmic modifications and also a (scalar-tensor) gravitational soliton. This may also be viewed as a static self-gravitating boson star in purely tensorial Conformal Gravity.