A new conformal duality of spherically symmetric space-times

TL;DR

This paper introduces a conformal duality transformation linking spherically symmetric solutions of conformal Weyl gravity to Einstein spaces, resolving longstanding debates and providing new insights into the structure of these solutions.

Contribution

It establishes a novel conformal duality that relates conformal Weyl gravity solutions to Einstein spaces, clarifying their connection and resolving previous controversies.

Findings

Every spherically symmetric solution of conformal Weyl gravity is conformally related to an Einstein space.

Provided an example of a spherically symmetric Einstein space as a limit of Schwarzschild-de Sitter spaces.

Resolved long-standing controversies regarding the structure of these space-times.

Abstract

A contribution linear in r to the gravitational potential can be created by a suitable conformal duality transformation: the conformal factor is 1/(1+r)^2 and r will be replaced by r/(1+r), where r is the Schwarzschild radial coordinate. Thus, every spherically symmetric solution of conformal Weyl gravity is conformally related to an Einstein space. This result finally resolves a long controversy about this topic. As a byproduct, we present an example of a spherically symmetric Einstein space which is a limit of a sequence of Schwarzschild-de Sitter space-times but which fails to be expressable in Schwarzschild coordinates. This example also resolves a long controversy.