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Solutions of the Geodesic Deviation Equation Obtained by Using Hidden Symmetries

P. Dolan and N. S. Swaminarayan
Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences
Vol. 84A, No. 2 (1984), pp. 133-139
Published by: Royal Irish Academy
Stable URL: http://www.jstor.org/stable/20489200
Page Count: 7
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Solutions of the Geodesic Deviation Equation Obtained by Using Hidden Symmetries
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Abstract

Very few exact solutions of the geodesic deviation equation are given in the general relativity literature even though they are important in the discussion of the gravitational tidal forces. With the aid of an irreducible Killing tensor $\xi _{ij}$ (or a hidden symmetry) it is possible to obtain new exact solutions. In this paper we show that the geodesics on a triaxial ellipsoid and the time-like geodesics in all the space-times of the Carter class possess exact solutions of the geodesic deviation equations due to the existence of the Killing tensor $\xi _{ij}$.

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