Re: invariance of negative signature of the metric?
- From: Tom Roberts <tjroberts137@xxxxxxxxxxxxx>
- Date: Fri, 07 Mar 2008 10:12:34 -0600
iuval 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?
This is more basic than the Einstein field equation -- one cannot have a CONTINUOUS manifold with a metric whose signature varies over the manifold. GR of course requires a continuous (Hausdorf, etc.) manifold.
Note the signature of a Lorentzian manifold can be either +2 or -2 (-+++ or +---), depending on one's sign convention. This does not affect the above statement (or the physical predictions of the theory), as one must select a single sign convention throughout the analysis.
Tom Roberts
.
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