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Re: Rayon Of Schwarschild

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Posted by Bruce on January 7, 2001 23:20:33 UTC

Its simple to understand how Newton would do it and more difficult to understand the GR derivation which renders the same resultant.
Newton
GMm/r=1/2mv^2
v^2=2GM/r
Since the event horizon is where the escape velocity would be c substitute c^2 for v^2.
r=2GM/c^2
It works out that r=2M when you express mass M in geometric units.
The curvature at r=2M is infinite as reckoned from the far away observer perspective
drshell=dr/(1-2M/r)^1/2
The local shell observer takes the integral of the above expression to show the distance r=2M+dr to r=2M is finite.
Where the curvature goes to infinite is at the singularity. GR can't describe these physics because the description for the singularity requires a marriage of quantum physics and relativity. This is what string theory (quantum gravity)is all about.

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