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arXiv · 1805.06326

Schwarzschild and linear potentials in Mannheim's model of conformal gravity

Peter R. Phillips
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Abstract

We study the equations of conformal gravity, as given by Mannheim, in the weak field limit, so that a linear approximation is adequate. Specializing to static fields with spherical symmetry, we obtain a second-order equation for one of the metric functions. We obtain the Green function for this equation, and represent the metric function in the form of integrals over the source. Near a compact source such as the Sun the solution no longer has Schwarzschild form. We conclude that a solution of Mannheim type cannot exist for these field equations.

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Peter R. Phillips. 2018-11-13. Schwarzschild and linear potentials in Mannheim's model of conformal gravity. https://doi.org/10.1093/mnras%2Fsty1286

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