Generalized Eddington--Finkelstein Coordinates and Exact Vaidya-Type Solutions in Weyl Conformal Gravity

TL;DR

This paper derives and analyzes exact Vaidya-type solutions in Weyl conformal gravity with various symmetries, revealing their complex structure and differences from general relativity, including properties like singularities, horizons, and gauge relations.

Contribution

It provides the first comprehensive classification of dynamical solutions in Weyl conformal gravity with spherical, hyperbolic, and planar symmetries, extending known solutions and analyzing their properties.

Findings

All vacuum dynamical solutions for specified symmetries are found.

Non-vacuum solutions with electric fields and null dust are classified.

Relations to Einstein spaces and implications of the Birkhoff--Riegert theorem are discussed.

Abstract

We study Vaidya-type solutions in Weyl conformal gravity (WCG) using Eddington--Finkelstein-like coordinates. Our considerations focus on spherical as well as hyperbolic and planar symmetries. In particular, we find all vacuum dynamical solutions for the aforementioned symmetries. These are, in contrast to general relativity, structurally quite non-trivial. We provide a thorough analysis of their basic properties, such as, relation to other known WCG solutions, algebraic types, singularities, horizons, and symmetries. In the same vein, we also derive, classify, and discuss non-vacuum solutions with the Coulombic electric field and null dust. Other salient issues, such as the gauge equivalence of WCG solutions to Einstein spaces and the role of the Birkhoff--Riegert theorem, are also addressed.