Re: PROOF: Schwarzschild Radius r=2*G*M/c^2 is wrong

On Sep 9, 11:41 pm, JanPB <film...@xxxxxxxxx> wrote:
On Sep 9, 9:18 pm, Koobee Wublee <koobee.wub...@xxxxxxxxx> wrote:

I am not changing the geometry. All the mathematics I have shown is
based on the invariance in the geometry. <shrug>

Eric - remember Koobee has his own private terminology for everything.

Again, I am not changing the geometry. All the mathematics I have
shown is
based on the invariance in the geometry. <shrug>

Also, you can always find
solutions that are static and spherically symmetric but not
asymptotically flat. Thus, this invalidates Birkhoff's theorem in
which you have bet all your chips on. <shrug>

Name one.

I have shown such two in this post below replying to your comment.

http://groups.google.com/group/sci.physics.relativity/msg/f812a0b372722b40?hl=en&;

With the following errata,

The Schwarzschild's original solution is when

** R = (r^3 + K^3)^(1/3) - K

The two solutions that are not asymptotically flat are when

** R = r / (1 + r^2 / K / L)

** R = r / (1 + r^2 / K / L + r^3 / K / L / N)

Where

** ds^2 = c^2 dt^2 / (1 + K / R) - (1 + K / R) (dR/dr)^2 dr^2 - (R +
K)^2 dO^2

Have you not read my postings before replying?

Since there are infinite choices of coordinate systems, there exist
infinite coordinate transformations of the same invariant geometry.
However, this is not what I am addressing. I need to establish a
choice of coordinate system before I can proceed to derive the
Christoffel symbols of the second kind. Thus, the choice of
coordinate system must be fixed at this point. Then, we see the
Riemann curvature tensor, the Ricci curvature tensor, the field
equations, and finally the metrics (solutions). In doing so, the
choice of coordinate system must remain the same throughout each
process.

You phrase it extraordinarily clumsily and in a typical amateurish
overcomplicated fashion but agreed so far.

Since there are an infinite number of solutions to the same
choice of coordinate system,

No, this is false in _this particular case_. In general yes, an
equation may have many solutions but the peculiarity of the
spherically symmetric vacuum problem is that it happens to lead to
equations which are guaranteed to have unique solution by virtue of
the general class of differential equations to which they happen to
belong.

Then, you are contradicting with yourself. You have agreed that the
coordinate system must be already established even before the
Christoffel symbols of the second kind are computed. At the solution
level, the choice of coordinate system should be the same as the
original choice chosen before the Christoffel symbols of the second
kind are computed. Since each solution or metric must be only applied
to the same choice of coordinate system, each solution or metric must
represent a different unique and independent geometry. You need to
resolve your own contradiction before we can go on further.

.

Relevant Pages

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  • Re: PROOF: Schwarzschild Radius r=2*G*M/c^2 is wrong
    ... spherically symmetric but not necessarily asymptotically flat. ... I am not changing the geometry. ... coordinate system must be fixed at this point. ...
    (sci.physics.relativity)
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    ... coordinate system, each solution or metric must describe a different ... and independent set of geometry. ... Einstein tensor? ... worse than I. <shrug> ...
    (sci.physics.relativity)