With commuting Killing vectors, the lapse and shift of one Killing vector are constants along the other

Details With commuting Killing vectors, the lapse and shift of one Killing vector are constants along the other With commuting Killing vectors, the lapse and shift of one Killing vector are constants along the other

2008-10-02

arxiv.org/abs/0810.0505v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

The key result in this paper was previously discovered by Beig and Chrusciel using a different approach. I add the appropriate

Scientific paper

Given an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shift of the second Killing vector, relative to this slice, remain constant along the orbits of the `surface' Killing vector. Alternatively, the six dot products that can be formed from the three vectors, the two Killing vectors and the normal to the submanifold, are all constants along the `surface' Killing vector.

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