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On the generalized Jacobi equation.

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On the generalized Jacobi equation. / Perlick, Volker.
In: General Relativity and Gravitation, Vol. 40, No. 5, 05.2008, p. 1029-1045.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Perlick, V 2008, 'On the generalized Jacobi equation.', General Relativity and Gravitation, vol. 40, no. 5, pp. 1029-1045. https://doi.org/10.1007/s10714-007-0589-x

APA

Perlick, V. (2008). On the generalized Jacobi equation. General Relativity and Gravitation, 40(5), 1029-1045. https://doi.org/10.1007/s10714-007-0589-x

Vancouver

Perlick V. On the generalized Jacobi equation. General Relativity and Gravitation. 2008 May;40(5):1029-1045. doi: 10.1007/s10714-007-0589-x

Author

Perlick, Volker. / On the generalized Jacobi equation. In: General Relativity and Gravitation. 2008 ; Vol. 40, No. 5. pp. 1029-1045.

Bibtex

@article{5f72e17d243c412681dece453437ae2f,
title = "On the generalized Jacobi equation.",
abstract = "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.",
keywords = "General relativity - Light rays - Jacobi equation",
author = "Volker Perlick",
year = "2008",
month = may,
doi = "10.1007/s10714-007-0589-x",
language = "English",
volume = "40",
pages = "1029--1045",
journal = "General Relativity and Gravitation",
issn = "0001-7701",
publisher = "Springer New York",
number = "5",

}

RIS

TY - JOUR

T1 - On the generalized Jacobi equation.

AU - Perlick, Volker

PY - 2008/5

Y1 - 2008/5

N2 - 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.

AB - 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.

KW - General relativity - Light rays - Jacobi equation

U2 - 10.1007/s10714-007-0589-x

DO - 10.1007/s10714-007-0589-x

M3 - Journal article

VL - 40

SP - 1029

EP - 1045

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

SN - 0001-7701

IS - 5

ER -