Jacobi-Maupertuis-Eisenhart metric and geodesic flows

Abstract

The Jacobi metric derived from the line element by one of the authors is shown to reduce to the standard formulation in the non-relativistic approximation. We obtain the Jacobi metric for various stationary metrics. Finally, the Jacobi-Maupertuis metric is formulated for time-dependent metrics by including the Eisenhart-Duval lift, known as the Jacobi-Eisenhart metric.

22 pages

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• Kerr black hole surrounded by a cloud of strings and its weak gravitational lensing in Rastall gravity
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