On integrability of the geodesic deviation equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10390160" target="_blank" >RIV/00216208:11320/18:10390160 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1140/epjc/s10052-018-6133-1" target="_blank" >https://doi.org/10.1140/epjc/s10052-018-6133-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1140/epjc/s10052-018-6133-1" target="_blank" >10.1140/epjc/s10052-018-6133-1</a>
Alternative languages
Result language
angličtina
Original language name
On integrability of the geodesic deviation equation
Original language 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10300 - Physical sciences
Result continuities
Project
<a href="/en/project/GB14-37086G" target="_blank" >GB14-37086G: Albert Einstein Center for Gravitation and Astrophysics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
European Physical Journal C
ISSN
1434-6044
e-ISSN
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Volume of the periodical
78
Issue of the periodical within the volume
8
Country of publishing house
DE - GERMANY
Number of pages
17
Pages from-to
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UT code for WoS article
000441930700002
EID of the result in the Scopus database
2-s2.0-85052204937