Spacetime "continuations"

[PPARKER@TWSUVM.UC.TWSU.EDU]

> Date: Fri, 3 May 96 12:42:50 -0400
> From: Bowman_David/tiger_mpc@tiger.gtc.georgetown.ky.us
[snip]
> possible inside the event horizon.  If a more complicated type of BH is being
> considered (i.e. one with sufficient angular momentum and/or charge) then
> there are analytic extensions to the home spacetime (region) of the observer
[snip]

This incidental comment prompts me to ask some questions about one of the
things mentioned. I address them to the list in general, but especially
to our resident GR experts.

Q1: What is the physical motivation for wanting or requiring (or whatever)
the extension to be analytic (as opposed to any lesser notion of smoothness,
such as C^\infty)?

Q2: What is the physical motivation for considering only extensions by
(analytic or otherwise) continuation of coordinates? Many other extension
procedures are known in differential geometry/topology, some of which
are independent of coordinate choices.

Q3: Even in the restricted context of analytic continuation of coordinates,
I do not really understand how the choice of which coordinates are to be
continued is made. For example, one can choose polar coordinates on flat
Minkowski spacetime and apply the analytic continuation procedure to obtain
a "helical" spacetime. Why is this not physically viable? (I assume it is not,
because I've never seen this example discussed in print.)

*************************
Phil Parker                          Internet: pparker@twsuvm.uc.twsu.edu
Math. Dept., Wichita St. Univ.         Bitnet: pparker@twsuvm
[Do not] put too much confidence in experimental results until they have
been confirmed by theory.---Sir Arthur Eddington