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An intrinsic characterization of the Schwarzschild metric. (English) Zbl 0937.83006
The paper describes a characterization of every type-D static vacuum solution of the Einstein equations, in terms of the metric tensor and some of its differential concomitants. As an application, the Schwarzschild solution is characterized by intrinsic and explicit conditions.

MSC:
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
83C15 Exact solutions to problems in general relativity and gravitational theory
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