Cariglia, MarcoHouri, TsuyoshiKrtous, PavelKubiznak, David2019-06-072019-06-072018CARILIGA, M. et al. On integrability of the geodesic deviation equation. European Physical Journal C, v. 71, n. 661, p. 1-17. Disponível em: <https://link.springer.com/article/10.1140/epjc/s10052-018-6133-1>. Acesso em: 19 mar. 2019.1434-6052http://www.repositorio.ufop.br/handle/123456789/11481The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we showhowone 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.en-USabertoArtigo publicado em periodicoThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Fonte: The European Physical Journal C <https://link.springer.com/article/10.1140/epjc/s10052-018-6133-1#copyrightInformation>. Acesso em: 11 abr. 2018.https://doi.org/10.1140/epjc/s10052-018-6133-1