Re: Misinterpretation of the radial parameter in the Schwarzschild solution - a response from Stephen Crothers.


Tom Roberts wrote:
LEJ Brouwer wrote:
Why not wish for a solution to Maxwell's equations that has
nonzero divergence of B? -- what you are asking for is
every bit as unreasonable, mathematically.

Because this would require a physically impossible rotational motion of
the luminiferous aether around the position of the magnetic monopole.

As I have said so often before,

Indeed a Tom Roberts 'trademark' no less.

just because you personally WISH for a
solution that is static everywhere does not mean that one exists.

Yes it does, because I am special and my wishes can come true.

Indeed, the combined requirements of spherical symmetry, vacuum outside
a point mass, and static everywhere, are inconsistent with the field
equation. Your wishes do not alter this fact.

Yes they do.

You are trying to discuss "points in space" that "feel like" they are
"infalling" -- this is IMHO part of your difficulty: GR does not have
any "points in space", but rather there are only points in spaceTIME.
So, for instance, in Schw. spacetime ignoring the angle coordinates,
there is a single point at (r=M/2,t=0), and it is completely unrelated
to the point at (r=M/2-epsilon,t=0+epsilon) -- the notion that somehow
these two points are a "single point of space being sucked in" is just
plain wrong -- they are TWO DISTINCT POINTS IN THE MANIFOLD.

Yes, yes, yes - we've been through all this before - and I know where
you are coming from, and I have agreed that you or Joe Bloggs can show
me all the maths you like to present your case and I won't disagree
with it, but I STILL think there is a qualitative difference between
the interior and the exterior of the event horizon, and that these two
regions are being glued together in an unnatural way, and I also think
that the Schwarzschild coordinates are special (mainly because of the
orthogonality of space and time - which I suspect is a real physical
property and not just an arbitrary coordinate condition), and I don't
like the way light cones do somersaults across the event horizon. With
a wave of my fairy godmother's magic wand, I say, throw away the
interior manifold, stick the singularity at the event horizon where it
belongs, and let the singularity act as a reflecting barrier which
bounces anything that hits it back out both spatially and temporally.
You are welcome to think what you like and hurl your usual abuse, but
to me this picture makes a lot more sense. And as you can see, my wish
has come true.

.