Re: invariance of negative signature of the metric?

iuval <clejan@xxxxxxxxxxxxxx> wrote:
Is there a theorem saying that if the metric starts out with a
negative signature on a spacelike surface (one or three eigenvalues
negative) that the field equations will preserve this negative
signature for all future and past?

There's some debate about this -- the answer depends on the
details of how you define the field equations. A signature change
necessarily means that the metric becomes degenerate on some
surface, and the Einstein field equations are usually derived
with the assumption of a nondegenerate metric. But the type of
degeneracy required is fairly mild, and there are extensions of
the field equations to cover such situations. The problem is that
the extension is not unique, and different choices give different
answers to your question.

See http://arxiv.org/abs/gr-qc/0012047 for a discussion and some
references.

Steve Carlip
.

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