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

On Tue, 17 Oct 2006 21:08:06 -0700, LEJ Brouwer wrote:


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.

Since there is, at present, no way even in principle to actually probe
anything beyond the event horizon (and get the results back, minor but
important point), _all_ we have for the interior is a mathematical model.
So, you may think what you like of the interior of black holes, and the
best anyone can do to test your thoughts on the subject is to compare them
with the behavior of the _model_ of a black hole in GRT. Beyond that,
nobody can say with certainty that you are wrong.

This, one could reasonably assert, puts that part of the discussion into
the realm of mathematics or philosophy, rather than physics.

If, eventually, some way is found to actually test what's what beyond the
event horizon -- by observing what comes out after a black hole
disintegrates, for instance -- then we may be able to obtain some real
answers as to what's beyond the horizon, and then discussions of what goes
on inside will be back in the realm of physics.

Personally my suspicion is that nature abhors singularities, and if a
theory has a singularity in it, there's probably a mismatch with reality
there someplace. Like uncountable infinities, singularities are useful
concepts but I won't hold my breath waiting for somebody to discover a
real instance of one.


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