Potential surfaces for time-like geodesics in the Curzon metric |
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Authors: | Fernando de Felice |
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Institution: | (1) Lagrange Institute of Mathematical Physics, University of Turin, Pvia C. Alberto 10, 10123 Torino, Italy |
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Abstract: | 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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