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Schwarzchild Inside the Event Horizon



 
 
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  #1  
Old August 3rd 11, 11:06 AM posted to sci.physics.relativity,sci.physics,sci.astro
mathematician
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Posts: 150
Default 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.

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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

  #2  
Old August 3rd 11, 06:00 PM posted to sci.physics.relativity,sci.physics,sci.astro
Tom Roberts[_2_]
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Posts: 49
Default 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
  #3  
Old August 3rd 11, 10:24 PM posted to sci.physics.relativity,sci.physics,sci.astro
eric gisse
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Posts: 303
Default 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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