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Global world functions. (English) Zbl 1086.53088

For Riemannian and pseudo-Riemannian spaces, the authors rediscuss Synge’s world function, which is an integral along a geodesic connecting two points. Especially, they mention the case of non-uniqueness of Synge’s function, which appears, if these two points can be joined by more than one geodesic. The main part of the paper is the reformulation of that integral by use of a Hamiltonian and introduction of auxiliary parameters.

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C22 Geodesics in global differential geometry
83C10 Equations of motion in general relativity and gravitational theory
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