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

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'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
.

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