Potential surfaces for time-like geodesics in the Curzon metric

Details Potential surfaces for time-like geodesics in the Curzon metric Potential surfaces for time-like geodesics in the Curzon metric

Feb 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991gregr..23..135d&link_type=abstract

General Relativity and Gravitation, Volume 23, Issue 2, pp.135-149

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Scientific paper

In this paper we deduce the general pattern of the potential surfaces for time-like geodesics in the Curzon metric. We find that for fairly small energies and orbital angular momenta, the time-like geodesics group into two sets; the geodesics of one set tend to thez-axis asR=(r2+z2)1/2→ 0,R=0 being a directional singularity, the others tend to ther-axis. At low energies these two sets are detached but they merge together as the energy increases. Stable circular motion is confined to thez = 0-plane and an energy threshold for stationary motion exists and is equal (per unit of rest-mass energy) to ≈ 0.945, a value almost indistinguishable from that in the Schwarzschild space-time.

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