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Publikace ÚTF

On integrability of the geodesic deviation equation

Cariglia, M., Houri, T., Krtouš, P., Kubizňák, D.

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
journal:European Physical Journal C
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