Re: black holes and singularity

From: Ken S. Tucker (dynamics_at_vianet.on.ca)
Date: 11/11/04 

Date: 10 Nov 2004 19:17:22 -0800

carlip-nospam@physics.ucdavis.edu wrote in message news:<cmtoms$s5l$1@skeeter.ucdavis.edu>...
> Ken S. Tucker <dynamics@vianet.on.ca> wrote:
>
> [...]
> > To be a bit more precise, consider the
>
> > g = det|g_uv|.
>
> > When that is zero, relativity does NOT apply.
>
> > The g=0 singularity is a haul mark of BH theory,
>
> It is not! g is not zero at a black hole horizon.
> It's perfectly well-behaved and finite.

Here's my reasoning, the det of g_uv
for 0,1 is adequate for my needs,

   g = | g_00 g_01 |
       | g_10 g_11 |

Select a CS where

   g = 1 - v^2/c^2 , g_01 = g_10 = -v/c

when v=c, g=0 as it should. "g" being a tensor
vanishes in all valid CS's. This proves the
event horizon is a CS figment, and is not
generally covariant.

Another way to see that is to examine the
transformation of the invariant dV,

   dV' = sqrt(g') dX'^1 ...dX'^n = dV

and note a rigid rod parallel to the radius
has zero length at the "horizon", i.e. dX=0.

>Nor are the
> tidal forces on a freely falling body particularly
> large, unless the black hole is extremely small.

Any generally covariant CS must use the event
horizon as "r = zero" due to the contraction of
the d(radius) to zero there. Therefore,

as r => 0, the tidal term,

  d^2 g_00/dr = -4m/r^3 => oo
 
> Where do you get this stuff?

It's all experimentally verified.
 The reason for the deflection of light to be
twice what is calculated based on "g_00" alone
is due to an equal amount more due to the
spatial warp described by "g_11". In GR the
radius "R" is related to Newtons "r" by,

  R = r - m , where m = 1.47 kilometers.

That means the path of a light ray will
be 1.47 km closer to the sun than Newton
would have predicted.

  Newton's "r" is consistent with the simple
pythagorean relation r^2=x^+y^+z^2, which
is only physically valid in the absence of
matter, and is used as a reference to gauge
the effect of matter, in light deflection and
Shapiro's experiments.
 
> Steve Carlip

Regards
Ken S. Tucker

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