Geodesics in stationary spacetimes. Application to Kerr spacetime

Details Geodesics in stationary spacetimes. Application to Kerr spacetime Geodesics in stationary spacetimes. Application to Kerr spacetime

2001-06-20

arxiv.org/abs/math/0106174v2

Mathematics

Differential Geometry

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

Scientific paper

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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