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Date: Tue, 14 May 1996 12:39:28 EST
From: "Paul Camp" <pjcamp@coastal.edu>
The motivations for analytic contiunation are mostly mathematical --
analyticity is a necessary and sufficient condition for geodesic
completeness.
The reason you need the continuation to be analytic isNo, I need only C^2 (twice continuously differentiable) to make good
because otherwise you cannot write down the geodesic equation, a
second order differential equation.
For a throoughly confusingI don't doubt their confusion here, but please supply a precise
account of this, see Hawking and Ellis Large Scale Structure of
Spacetime.
Which coordinates do you choose to extend? Whichever look like theyOK, let's assume for now that the objective is to extend to a
may be extendable. For a black hole, only maximal extension of the
Kruskal coordinates provides geodesic completeness.
Minkowski spacetime is already geodesically complete andI don't remember their proof, but using the embedding definition of
so cannot be further extended. The proof of this is in the Hawking
and Ellis book but you really don't want to see it. Trust me.