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A new conformal duality of spherically symmetric space-times

H. -J. Schmidt
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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.

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H. -J. Schmidt. 1999-05-28. A new conformal duality of spherically symmetric space-times. https://arxiv.org/abs/gr-qc/9905103

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