Geodesics for the NUT metric and gravitational monopoles

Details Geodesics for the NUT metric and gravitational monopoles Geodesics for the NUT metric and gravitational monopoles

Aug 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989gregr..21..821z&link_type=abstract

General Relativity and Gravitation, Volume 21, Issue 8, pp.821-848

Physics

14

Scientific paper

In order to provide insight about the physical interpretation of the NUT parameter, we solve the geodesic equations for the NUT metric. We show that the properties of NUT geodesics are similar to the properties of trajectories for charged particles orbiting about a magnetic monopole. In summary, we show that (1) the orbits lie on the surface of a cone, (2) the conserved total angular momentum is the sum of the orbital angular momentum plus the angular momentum due to the “monopole” field, (3) the monopole field angular momentum is independent of the separation between the source of the gravitational field and the test particle, and (4) the geodesics are “almost” spherically symmetric. The strong similarities between the NUT geodesics and the electromagnetic monopole suggest that the NUT metric is an exact solution for a gravitational magnetic monopole. However, the subtle difference of being only almost spherically symmetric implies that the analogy is not perfect. The almost spherically symmetric nature of the NUT geodesics suggest that the energy of the “Dirac string” makes a contribution to the solution. We also construct exact solutions for special orbits, discuss a twin paradox, and speculate about the Dirac quantization condition for a gravitational magnetic monopole.

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