A scalar geodesic deviation equation and a phase theorem

P. Choudhury, P. Dolan and N. S. Swaminarayan

International Journal of Mathematics and Mathematical Sciences, 1983, vol. 6, 1-8

Abstract:

A scalar equation is derived for η , the distance between two structureless test particles falling freely in a gravitational field: η ¨ + ( K − Ω 2 ) η = 0 . An amplitude, frequency and a phase are defined for the relative motion. The phases are classed as elliptic, hyperbolic and parabolic according as K − Ω 2 > 0 , < 0 , = 0. In elliptic phases we deduce a positive definite relative energy E and a phase-shift theorem. The relevance of the phase-shift theorem to gravitational plane waves is discussed.

Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:427949

DOI: 10.1155/S0161171283000678

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