Abstract
Synge (1966) and Zeldovich and Novikov (1978) have discussed the gravitational trapping of zero rest-mass particles in Schwarzschild geometry. Durgapal and Pande (1979) and Pande and Durgapal (1986) extended this method to the interior geometries as well. For non-zero rest-mass particles the motion has been discussed in Schwarzschild geometries for vacuum metrics. In the present work a general method has been developed by which the motion (in particular the gravitational trapping) of non-zero rest-mass particles may be studied in any given static spherical space time geometry. The method has been illustrated by considering the geometries pertaining to Tolman's III, IV, and V solutions respectively. The limiting case of this study (i.e., when rest-mass approaches zero) gives the relevant expressions for the zero rest-mass particles as discussed earlier by Durgapal and Pande. This method may find application to the motion of bodies in relativistic clusters and in compact objects like quasars and active galactic nuclei.
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