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The asymptotic of static isolated systems and a generalized uniqueness for Schwarzschild

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Reiris,  Martin
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1501.01180.pdf
(Preprint), 162KB

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Citation

Reiris, M. (2015). The asymptotic of static isolated systems and a generalized uniqueness for Schwarzschild. Classical and quantum gravity, 32(19): 195001. doi:10.1088/0264-9381/32/19/195001.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0028-FE37-E
Abstract
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^3 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.