ar X iv : 1 50 1 . 01 18 0 v 1 [ gr - q c ] 6 J an 2 01 5 The asymptotic of static isolated systems and a generalised uniqueness for Schwarzschild
نویسنده
چکیده
It is proved that any static system that is spacetime-geodesically complete at infinity, and whose spacelike-topology outside a compact set is that of R minus a ball, is asymptotically flat. The matter is assumed compactly supported and no energy condition is required. A similar (though stronger) result applies to black holes too. This allows us to state a large generalisation of the uniqueness of the Schwarzschild solution not requiring asymptotic flatness. The Korotkin-Nicolai static black-hole shows that, for the given generalisation, no further flexibility in the hypothesis is possible.
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