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Geodesics around Weyl-Bach's Ring Solution

L. A. D'Afonseca·P. S. Letelier·S. R. Oliveira
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Abstract

We explore some of the gravitational features of a uniform ring both in the Newtonian potential theory and in General Relativity. We use a spacetime associated to a Weyl static solution of the vacuum Einstein's equations with ring like singularity. The Newtonian motion for a test particle in the gravitational field of the ring is studied and compared with the corresponding geodesic motion in the given spacetime. We have found a relativistic peculiar attraction: free falling particle geodesics are lead to the inner rim but never hit the ring.

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L. A. D'Afonseca, P. S. Letelier, S. R. Oliveira. 2005-08-18. Geodesics around Weyl-Bach's Ring Solution. https://doi.org/10.1088/0264-9381%2F22%2F17%2F028

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