On the generalized Jacobi equation.

Perlick, Volker (2008) On the generalized Jacobi equation. General Relativity and Gravitation, 40 (5). pp. 1029-1045. ISSN 0001-7701

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The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The generalized Jacobi equation, introduced by Hodgkinson in 1972 and further developed by Mashhoon and others, arises if the linearization is done only with respect to the coordinates, but not with respect to the velocities. The resulting equation has been studied by several authors in some detail for timelike geodesics in a Lorentzian manifold. Here we begin by briefly considering the generalized Jacobi equation on affine manifolds, without a metric; then we specify to lightlike geodesics in a Lorentzian manifold. We illustrate the latter case by considering particular lightlike geodesics (a) in Schwarzschild spacetime and (b) in a plane-wave spacetime.

Item Type:
Journal Article
Journal or Publication Title:
General Relativity and Gravitation
Uncontrolled Keywords:
?? general relativity - light rays - jacobi equationphysics and astronomy (miscellaneous)qc physics ??
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Deposited On:
13 Aug 2008 10:45
Last Modified:
13 Apr 2024 23:53