Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem

Details Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem

1995-10-10

arxiv.org/abs/gr-qc/9510015v3

J.Math.Phys. 37 (1996) 1939-1961

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages

Scientific paper

10.1063/1.531497

We study Killing vector fields in asymptotically flat space-times. We prove the following result, implicitly assumed in the uniqueness theory of stationary black holes. If the conditions of the rigidity part of the positive energy theorem are met, then in such space-times there are no asymptotically null Killing vector fields except if the initial data set can be embedded in Minkowski space-time. We also give a proof of the non-existence of non-singular (in an appropriate sense) asymptotically flat space-times which satisfy an energy condition and which have a null ADM four-momentum, under conditions weaker than previously considered.

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