Geodesics around Weyl-Bach's Ring Solution

Details Geodesics around Weyl-Bach's Ring Solution Geodesics around Weyl-Bach's Ring Solution

2005-07-07

arxiv.org/abs/gr-qc/0507033v2

Class.Quant.Grav. 22 (2005) 3803-3814

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 figures, 14 pages. LaTeX w/ subfigure, graphicx

Scientific paper

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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