On integrability of the geodesic deviation equation.

Detalhes bibliográficos
Autor(a) principal: Cariglia, Marco
Data de Publicação: 2018
Outros Autores: Houri, Tsuyoshi, Krtous, Pavel, Kubiznak, David
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFOP
Texto Completo: http://www.repositorio.ufop.br/handle/123456789/11481
https://doi.org/10.1140/epjc/s10052-018-6133-1
Resumo: The 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.
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spelling Cariglia, MarcoHouri, TsuyoshiKrtous, PavelKubiznak, David2019-06-07T15:35:50Z2019-06-07T15:35:50Z2018CARILIGA, 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/123456789/11481https://doi.org/10.1140/epjc/s10052-018-6133-1The 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.This 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.info:eu-repo/semantics/openAccessOn integrability of the geodesic deviation equation.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOPLICENSElicense.txtlicense.txttext/plain; charset=utf-8924http://www.repositorio.ufop.br/bitstream/123456789/11481/2/license.txt62604f8d955274beb56c80ce1ee5dcaeMD52ORIGINALARTIGO_IntegrabilityGeodesicDeviation.pdfARTIGO_IntegrabilityGeodesicDeviation.pdfapplication/pdf524036http://www.repositorio.ufop.br/bitstream/123456789/11481/1/ARTIGO_IntegrabilityGeodesicDeviation.pdf0aeb413cb63d3500e2416bed9bae052cMD51123456789/114812019-06-07 11:35:50.925oai:localhost: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ório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332019-06-07T15:35:50Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false
dc.title.pt_BR.fl_str_mv On integrability of the geodesic deviation equation.
title On integrability of the geodesic deviation equation.
spellingShingle On integrability of the geodesic deviation equation.
Cariglia, Marco
title_short On integrability of the geodesic deviation equation.
title_full On integrability of the geodesic deviation equation.
title_fullStr On integrability of the geodesic deviation equation.
title_full_unstemmed On integrability of the geodesic deviation equation.
title_sort On integrability of the geodesic deviation equation.
author Cariglia, Marco
author_facet Cariglia, Marco
Houri, Tsuyoshi
Krtous, Pavel
Kubiznak, David
author_role author
author2 Houri, Tsuyoshi
Krtous, Pavel
Kubiznak, David
author2_role author
author
author
dc.contributor.author.fl_str_mv Cariglia, Marco
Houri, Tsuyoshi
Krtous, Pavel
Kubiznak, David
description The 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.
publishDate 2018
dc.date.issued.fl_str_mv 2018
dc.date.accessioned.fl_str_mv 2019-06-07T15:35:50Z
dc.date.available.fl_str_mv 2019-06-07T15:35:50Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.citation.fl_str_mv CARILIGA, 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.
dc.identifier.uri.fl_str_mv http://www.repositorio.ufop.br/handle/123456789/11481
dc.identifier.issn.none.fl_str_mv 1434-6052
dc.identifier.doi.pt_BR.fl_str_mv https://doi.org/10.1140/epjc/s10052-018-6133-1
identifier_str_mv CARILIGA, 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.
1434-6052
url http://www.repositorio.ufop.br/handle/123456789/11481
https://doi.org/10.1140/epjc/s10052-018-6133-1
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http://www.repositorio.ufop.br/bitstream/123456789/11481/1/ARTIGO_IntegrabilityGeodesicDeviation.pdf
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