Geodesics around Weyl-Bach's Ring Solution

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.

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

References in corpus (1)

• Global structure of the Zipoy-Voorhees-Weyl spacetime and the delta=2 Tomimatsu-Sato spacetime

Cited by in corpus (12)

• Free motion around black holes with discs or rings: between integrability and chaos - II
• Free motion around black holes with discs or rings: between integrability and chaos - I
• Free motion around black holes with discs or rings: between integrability and chaos -- IV
• Shadow of a Schwarzschild black hole surrounded by a Bach-Weyl ring
• Exact density-potential pairs from the holomorphic Coulomb field
• Static axisymmetric rings in general relativity: How diverse they are
• Exact density-potential pairs from complex shifted axisymmetric systems
• On geometry of deformed black holes: II. Schwarzschild hole surrounded by a Bach-Weyl ring
• Particle dynamics in the Newtonian potential sourced by a homogeneous circular ring
• Chaotic particle motion around a homogeneous circular ring
• Analytical potential-density pairs from complex-shifted Kuzmin-Toomre discs
• On geodesic dynamics in deformed black-hole fields