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Schwarzchild Inside the Event Horizon
I think that problem would be that in reality GR (General Relativity)
is not full 4-dimensional. GR is really (3+1)-dimensional and time dimension is different kind that three space dimensions as mentioned reference below. Arbitrary 4-dim coordinate transformations are not allowed in GR.. For example in reference below it is mentioned that it is not allowed to transform "meter stick" to "clock" and vice versa. Reference 1. Tolman,R.C, 1962. Relativity, Thermodynamics and Cosmology. Please take a look. Best Regards, Hannu Poropudas Vesaisentie 9E 90900 Kiiminki Finland hanporop @ luukku.com Reference 2. -------COPY BELOW--------------------------------------------------------------------------------------- From: Newsgroups: sci.physics.foundations Subject: Schwarzchild Inside the Event Horizon Date: Wed, 2 Jun 2010 18:21:28 CST Organization: Aioe.org NNTP Server Lines: 17 Approved: SPF Approval Key Message-ID: References: NNTP-Posting-Host: znSDP4EoeO+tgznwopQBwQ.user.speranza.aioe.org X-Complaints-To: Return-Path: X-SPF-Policy: http://stump.algebra.com/~spf X-SPF-Info-1: Send submissions to X-SPF-Info-2: Send complaints to X-Comment: moderators do not necessarily agree or disagree with this article. X-Robomod: STUMP, (Igor Chudov), C++/Perl/Unix Consulting X-Moderation-1: Hassle-Free commercial hosting of moderation sites available X-Moderation-2: See http://www.algebra.com/~ichudov/stump User-Agent: tin/1.8.3-20070201 ("Scotasay") (UNIX) (Linux/ 2.6.26.8-57.fc8 (i686)) X-Notice: Filtered by postfilter v. 0.8.2 FromStump: yes Mike_Fontenot wrote: A few months ago, I spent some time studying the Schwarzchild metric OUTSIDE the event horizon (EH). Lately, I've been studying that metric INSIDE the EH. The more I get into it, the stranger it seems. It might help to know that the Schwarzschild metric inside the horizon is equivalent to a collapsing Kantowski-Sachs cosmology. At a fixed time r, the universe is an infinite cylinder RxS^2; the radius of that cylinder descreases in time, and the singularity at r=0 is essentially a "crunch." There's a nice paper by Krasnikov at arxiv.org/abs/0804.3619, published in Gravitation and Cosmology 14 (2008) 362, that you may find helpful. Steve Carlip |
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Schwarzchild Inside the Event Horizon
On 8/3/11 8/3/11 - 5:06 AM, mathematician wrote:
I think that problem would be that in reality GR (General Relativity) is not full 4-dimensional. This is not true. GR is fully 4 dimensional, in the usual meanings of these words. That is, it requires a 4-d manifold to represent the world modeled by GR. GR is really (3+1)-dimensional and time dimension is different kind that three space dimensions as mentioned reference below. Yes, this is true. But this refers to the metric on the manifold, not to the manifold itself. The manifold has 4 dimensions, and the distinction between 4 and 3+1 does not apply to the manifold. The metric has signature (3,1), and with the common shortcut of saying "the manifold" when one means "the manifold with metric", one might say that GR has a (3+1)-d manifold -- that is a shortcut, not a rigorously true statement. Arbitrary 4-dim coordinate transformations are not allowed in GR.. Again not true. Any valid 4-d coordinate transform is permitted in GR. But no valid coordinate transform can change the signature of the metric. Here "valid" means non-singular everywhere within the region of validity of the coordinates in question; "non-singular" means having a nonzero and finite Jacobian -- that is equivalent to the transform and its inverse being well behaved throughout the region. Note that GR is not responsible for requiring "valid" coordinate transforms, that is a general property of geometry, and is part and parcel of the meaning of "coordinate system". A set of variables related to a coordinate system by a singular transform do not form a coordinate system. For example in reference below it is mentioned that it is not allowed to transform "meter stick" to "clock" and vice versa. Hmmmm. It's not clear what that means. Certainly any interval spanned by a meterstick has a spacelike character, and no coordinate transform can change that. Similarly, any interval spanned by a clock has a timelike character, and no coordinate transform can change that, either. A ruler is physically different from a clock, and no math can affect that. Indeed, no aspect of a model can affect objects in the world. Tom Roberts |
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Schwarzchild Inside the Event Horizon
mathematician wrote in
: I think that problem would be that in reality GR (General Relativity) is not full 4-dimensional. GR is really (3+1)-dimensional and time dimension is different kind that three space dimensions as mentioned reference below. Arbitrary 4-dim coordinate transformations are not allowed in GR.. Learn the theory before making **** up, Hannau. [...] |
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