Geodesics in stationary spacetimes. Application to Kerr spacetime

2001/06/20 by Jose Luis Flores, José Luis Flores, Miguel Sánchez +3
Mathematics · Physics and Astronomy · #53C22 #53C50 #83C15 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons #math.DG #msc:53C22 #msc:53C50 #msc:83C15

paper · pdf · doi:10.48550/arxiv.math/0106174

19 pages. To appear in Int. J. Theor. Phys

openalex publication_date 2001/06/20 · arxiv created 2002/01/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Levi-Civita connection and geodesic equations for a stationary spacetime are studied in depth. General formulae which generalize those for warped products are obtained. These results are applicated to some regions of Kerr spacetime previously studied by using variational methods. We show that they are neither space-convex nor geodesically connected. Moreover, the whole stationary part of Kerr spacetime is not geodesically connected, except when the angular momentum is equal to zero (Schwarzschild spacetime).

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