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

Reiris, Martin

doi:10.1088/0264-9381/32/19/195001

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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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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: https://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.