A scalar geodesic deviation equation and a phase theorem
A scalar equation is derived for η, the distance between two structureless test particles falling freely in a gravitational field: η¨+(K−Ω2)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−Ω2>...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171283000678 |
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| _version_ | 1850159677197778944 |
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| author | P. Choudhury P. Dolan N. S. Swaminarayan |
| author_facet | P. Choudhury P. Dolan N. S. Swaminarayan |
| author_sort | P. Choudhury |
| collection | DOAJ |
| description | A scalar equation is derived for η, the distance between two structureless test particles falling freely in a gravitational field:
η¨+(K−Ω2)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−Ω2>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. |
| format | Article |
| id | doaj-art-b32958b1becd4cbdba7138b1f6cd17c0 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b32958b1becd4cbdba7138b1f6cd17c02025-08-20T02:23:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016479580210.1155/S0161171283000678A scalar geodesic deviation equation and a phase theoremP. Choudhury0P. Dolan1N. S. Swaminarayan2Department of Mathematics, Imperial College, London SW7 2AZ, UKDepartment of Mathematics, Imperial College, London SW7 2AZ, UKDepartment of Mathematics, Auburn University, Alabama 36849, USAA scalar equation is derived for η, the distance between two structureless test particles falling freely in a gravitational field: η¨+(K−Ω2)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−Ω2>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.http://dx.doi.org/10.1155/S0161171283000678geodesic deviationgravitational radiation. |
| spellingShingle | P. Choudhury P. Dolan N. S. Swaminarayan A scalar geodesic deviation equation and a phase theorem International Journal of Mathematics and Mathematical Sciences geodesic deviation gravitational radiation. |
| title | A scalar geodesic deviation equation and a phase theorem |
| title_full | A scalar geodesic deviation equation and a phase theorem |
| title_fullStr | A scalar geodesic deviation equation and a phase theorem |
| title_full_unstemmed | A scalar geodesic deviation equation and a phase theorem |
| title_short | A scalar geodesic deviation equation and a phase theorem |
| title_sort | scalar geodesic deviation equation and a phase theorem |
| topic | geodesic deviation gravitational radiation. |
| url | http://dx.doi.org/10.1155/S0161171283000678 |
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