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

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

typ: | article |
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journal: | European Physical Journal C |

volume: | 78 |

pages: | 661 |

year: | 2018 |