Trajectories of nonzero-rest-mass particles in curved spacetime

Details Trajectories of nonzero-rest-mass particles in curved spacetime Trajectories of nonzero-rest-mass particles in curved spacetime

Mar 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...406....1n&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 406, no. 1, p. 1-5.

Mathematics

Metric Geometry

2

Galactic Clusters, Particle Mass, Particle Trajectories, Space-Time Functions, Stellar Motions, Dark Matter, Gravitational Effects, Mass Distribution

Scientific paper

A detailed study of the trajectory of a nonzero-rest-mass particle in a spherically symmetric geometry may distinguish a relativistic cluster from a Newtonian one. A general method for studying trajectories in a given geometry described by metric coefficients is presented in this paper. Exact NZRP trajectories for a geometry pertaining to Tolman's type IV solution are obtained and classified as (1) spiral trajectories with a constant inner cuvature, (2) looped trajectories, (3) trajectories with a cusp at the minimum distance, and (4) trajectories with an inner loop. The trajectories are compared with those of a zero-rest-mass particle in a similar geometry. Some examples of trajectories in other geometries are also given. These studies may be relevant to the motion of galaxies in relativistic clusters.

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