Re: Black hole with asymptotically flat interior

Hunter wrote: 
First, the exterior's embedding diagram is a surface of revolution of
a half parabola, an analytic function described by a convergent power
series, whose unique extension is the rest of the parabola. Under any
other extension, geodesics crossing r=2M are not analytic at r=2M.

Quite correct, but this is not the whole Schwarzschild geometry, just a slice of it. The paths into the genuine interior don't lie on this slice, so you can't see them on the embedding diagram -- just as when you use Schwarzschild coordinates, you can't see region III.

Second, any geodesic must be time symmetric because the Schwarzschild
metric is time symmetric.


Certainly not! The Minkowski metric is time symmetric (unchanged under
t <-> -t), but the geodesic x=ct, y=z=0 is not.

-- Ben
.