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Conformal geodesics on vacuum space-times. (English) Zbl 1040.53079
Some properties of conformal geodesics on general space-times, specialized to vacuum space-times are discussed. After specializing further to warped product vacuum space-times a conformal Gauss system on the Schwarzschild-Kruskal space-time is analyzed. Expressions for the conformal geodesics determined by suitably chosen initial data are derived in terms of elliptic and theta functions. It is shown that the curves extend smoothly through null infinity and that the associated conformal factor defines a smooth conformal extension if the congruence is regular.

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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