On integrability of the geodesic deviation equation View Full Text


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Article Info

DATE

2018-08

AUTHORS

Marco Cariglia, Tsuyoshi Houri, Pavel Krtouš, David Kubizňák

ABSTRACT

The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime admitting completely integrable geodesics. Namely, by linearizing the geodesic equation and its conserved charges, we arrive at the invariant Wronskians for the Jacobi system that are linear in the ‘deviation momenta’ and thus yield a system of first-order differential equations that can be integrated. The procedure is illustrated on an example of a rotating black hole spacetime described by the Kerr geometry and its higher-dimensional generalizations. A number of related topics, including the phase space formulation of the theory and the derivation of the covariant Hamiltonian for the Jacobi system are also discussed. More... »

PAGES

661

Identifiers

URI

http://scigraph.springernature.com/pub.10.1140/epjc/s10052-018-6133-1

DOI

http://dx.doi.org/10.1140/epjc/s10052-018-6133-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1106227117


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48 schema:description The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime admitting completely integrable geodesics. Namely, by linearizing the geodesic equation and its conserved charges, we arrive at the invariant Wronskians for the Jacobi system that are linear in the ‘deviation momenta’ and thus yield a system of first-order differential equations that can be integrated. The procedure is illustrated on an example of a rotating black hole spacetime described by the Kerr geometry and its higher-dimensional generalizations. A number of related topics, including the phase space formulation of the theory and the derivation of the covariant Hamiltonian for the Jacobi system are also discussed.
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