On integrability of the geodesic deviation equation.
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , |
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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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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eng |
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