Re: More on the controversy about the Schwarzschild radius and black holes.

On Apr 24, 5:04 pm, Ben Rudiak-Gould <br276delet...@xxxxxxxxx> wrote:
LEJ Brouwer wrote:
If you just look for vacuum solutions
with SO(3) symmetry, and make no prior assumptions about the nature of
r and t, then sure - it does not matter if integrating dr gives a
complex number, as Daryl pointed out. However, if you look for
solutions assuming a spherical matter distribution, and take a priori
the physical interpretations of r and t as spacelike and timelike
directions respectively (as is usually done in the textbooks), then
the integral of dr becoming complex does not make sense and is
physically incorrect, as Crothers states.

The fact that you wrote this an hour after responding to my last post makes
me think you didn't understand what I was trying to say. You still seem to
think that one can conclude something about a solution based on the
assumptions that went into its derivation. That's crazy talk. That's
postmodernism. In the real, scientific world, a solution is a satisfying
assignment. Even if you made an outright mistake in your derivation --
getting a sign wrong or writing x^0 for the antiderivative of x^-1 or using
complex numbers where only reals make sense -- even then, if what you end up
with is a satisfying assignment, then it's valid. I know you understand this
at some level, but I think at another level you don't. Otherwise you
wouldn't continue to harp on the derivation of the Schwarzschild solution,
as though that could possibly have any relevance to anything.

I guess what it boils down to is that I do not believe that all
coordinate choices have a meaningful physical interpretation. At a
very simplistic level, we all agree that x^2 = 9 has two solutions, +3
and -3, but I am claiming that the real problem is something like: if
the number of apples that John has is equal to the number of apples
Bob has squared, then how many apples does John have? Basically my
intuition tells me that 'background independent' GR, if I may call it
that, is too general and includes solutions which are not physically
sensible. In this particular case, my intuition is telling me that
something goes badly wrong at the event horizon.

I'm not saying your conclusion is wrong. I'm not even saying your intuition
is wrong. I'm just saying that your current attempt to formalize your
intuition makes no sense, and you're going to have to find a different one.
Perhaps what you're really concerned about is the *formation* of a black
hole; perhaps your intuition is that an initial spherically symmetric
configuration of matter can't dynamically evolve into something resembling
the r<2M portion of the Schwarzschild solution. That's a potentially
interesting line of argument, but it's not what you're arguing now. What
you're arguing now is silly.

-- Ben

Well, you are being more generous than your colleagues in that case!
Anyway, I am probably just doing a poor job of expressing in a clear
way what my intuition is telling me.

As it happens, I came across a very simple thermodynamic argument why
black holes cannot be formed from spherical collapse of ordinary
matter - thought that particular argument does not hold for photons or
gravitational waves (I do believe in the possibility of complete
gravitational collapse of the latter, but obviously not to form a
singularity). If I have some time later, I will give the details as it
was only a few lines and pretty easy to follow.

My personal opinion is that the Schwarzshild interior solution is
unphysical (that's not to say that there is not some other metric
describing the stuff which lies 'inside' the event horizon), and that
once the event horizon forms, it acts like a brick wall effectively
physically sealing off the interior from the exterior, so that
anything subsequently hitting the event horizon bounces of it both
spatially and temporally (so that it looks like particle-antiparticle
pairs are annihilating at the EH). The reasons I think this is the
case are rather involved, so I won't go into them now.

Having said, that it is of course possible that the standard view is
correct, (in which case I will insist that the singularity causes a
space-time reflection like the one described in the last paragraph!) -
I just have difficulties believing that the picture it paints can be
physically real.

Thanks,

Sabbir.

.

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