Conformal gravity and "gravitational bubbles"

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.

7 pages, Talk given at the 9th Alexander Friedmann International Seminar on Gravitation and Cosmology, June 21, 2015 - June 27, 2015, Saint Petersburg, Russia

References in corpus (1)

• Spherically symmetric conformal gravity and "gravitational bubbles"

Cited by in corpus (5)

• Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity
• Spherically symmetric double layers in Weyl+Einstein gravity
• Mass decomposition of SLACS lens galaxies in Weyl conformal gravity
• On the theory of spherically symmetric thin shells in conformal gravity
• Gravitational Surface Tension as the Origin for the Black Hole Entropy