v 1 2 8 M ay 1 99 9 A new conformal duality of spherically symmetric space – times

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) 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. ∗http://www.physik.fu-berlin.de/ ̃hjschmi e-mail: [email protected] Keyword(s): Alternative Theories of Gravity, Conformal invariance, spherical symmetry, Schwarzschild coordinates, Einstein spaces.