
doi: 10.1007/bf00968692
The Schwarzschild solution (internal as well as external) is considered and the universal covering of it is constructed. This implies the following: If a spacetime contains both internal and external domains and each radial geodesic is extendible through the Schwarzschild radius then either there exists a cycle (a closed timelike curve) or the exterior domain exists in many isometrical but distinct duplicates. The first violates the causality condition, and the second violates the uniqueness of the world. [In the English translation on page 780, line 14 above there must be read ''exterior'' instead of the printed ''interior''.]
Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Schwarzschild solution, universal covering, Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory, closed timelike curve, Applications of global differential geometry to the sciences, causality condition
Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Schwarzschild solution, universal covering, Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory, closed timelike curve, Applications of global differential geometry to the sciences, causality condition
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