-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Andy Latto Sent: Friday, July 24, 2009 3:18 PM To: math-fun Subject: Re: [math-fun] dumb question about general relativity On Fri, Jul 24, 2009 at 3:15 PM, Henry Baker <hbaker1@pipeline.com> wrote:
This question is about "classical" "infinitesimal" GR -- i.e., no quantum stuff like Hawking radiation & no Planck length.
The laws of GR are symmetric w.r.t. time, so we have the following conundrum:
If an object falls towards a black hole, from the perspective of an outside observer, time on the object gets slower & slower & in the limit it stops. I've been told that as a result of this time dilation, everything that "falls into" the black hole doesn't really fall in, but ends up getting painted onto its surface (from the perspective of the outside observer).
But if the laws are truly symmetric w.r.t. time, then it should be possible for the black hole to "burp" out objects, as well.
I don't think this is right. I think the right conclusion is that it should be possible for a different sort of object, a time-reversed black hole, that burps out objects, to exist. But it's wildly unlikely that any such object will come to exist, for entropic reasons.
Kruskal spacetime is the extension of a Schwarzschild Black Hole, I think. Note that, for a wormhole, you need spin or (possibly) charge in your black hole.
An analogy: if you break an egg, the fact that the laws of physics have time-reversal symmetry (or close enough for this example) doesn't mean that the pieces of eggshell will reform an egg. They mean that if the situation with all the egg fragments having exactly the negative of their current velocities happened, then they would form an egg. But in practice, we see eggs breaking, and not fragments reuniting, just as we see black holes but not white holes.
All of this presupposes some sort of invertible transform in going from the perspective of the outside observer to the observer on the moving object. But clearly, such an invertible transform has a singularity at the "time" when the object gets painted onto the black hole (from the outside observer's perspective).
I don't think there is such a time. I think that from the outside observer's perspective, the object gets exponentially closer to the event horizon with time, but never actually reaches it (Of course, when it gets within the Planck length, quantum-mechanical considerations will become relevant; but we're excluding those). So there is no singularity in finite time from the perspective of the outside observer.
The person falling in falls in (in his reference frame) quickly. An outside observer would see him asymptotically approach the event horizon, red-shifting more and more, but would not see him cross it. --
Andy.Latto@pobox.com
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