Conformal gravity and "gravitational bubbles"

TL;DR

This paper explores spherically symmetric solutions in Weyl conformal gravity, highlighting unique vacuum solutions called 'gravitational bubbles' that are impossible in General Relativity, and analyzing their structure and implications.

Contribution

It provides a complete classification of vacuum solutions in conformal gravity, introducing 'gravitational bubbles' and analyzing their properties and significance.

Findings

Identified vacuum solutions with zero Weyl tensor called 'gravitational bubbles'

Connected solutions to the Mannheim--Kazanas family via conformal transformations

Showed these solutions are absent in General Relativity, implying new universe creation scenarios.

Abstract

We describe the general structure of the spherically symmetric solutions in the Weyl conformal gravity. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions, consisting of two classes, is found. The first one contains the solutions with constant two-dimensional curvature scalar, and the representatives are the famous Robertson--Walker metrics. We called one of them the "gravitational bubbles", which is compact and with zero Weyl tensor. These "gravitational bubbles" are the pure vacuum curved space-times (without any material sources, including the cosmological constant), which are absolutely impossible in General Relativity. This phenomenon makes it easier to create the universe from "nothing". The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family, which can be conformally covered by the thee-parameter Mannheim--Kazanas solution. We describe the general structure of the energy-momentum tensor in the spherical conformal gravity and construct the vectorial equation that reveals clearly some features of non-vacuum solutions.