Abstract
We study focal points and Maslov index of a horizontal geodesic γ : I → M in the total space of a semi-Riemannian submersion π : M → B by determining an explicit relation with the corresponding objects along the projected geodesic \({\pi\circ\gamma:I\to B}\) in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.
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Caponio, E., Javaloyes, M.A. & Piccione, P. Maslov index in semi-Riemannian submersions. Ann Glob Anal Geom 38, 57–75 (2010). https://doi.org/10.1007/s10455-010-9200-x
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DOI: https://doi.org/10.1007/s10455-010-9200-x