Schwarzschild and Newton potential

[Passionflower]

Expressing the Schwarzschild in the Weyl form allows one to use the Newton potential. The Newton potential here is, perhaps surprisingly, equivalent with a rod of length 2M and mass M. Also the rod is exactly positioned where r = 2M. Furthermore if we decrease the length of the rod to the solution of a point mass, the solution is no longer spherically symmetric.

What, if anything, do you think is the significance of all this?

Fair question: Does the Schwarzschild solution refer to a removed rod or to a removed point mass?

 

[Altabeh]

Expressing the Schwarzschild in the Weyl form allows one to use the Newton potential. The Newton potential here is, perhaps surprisingly, equivalent with a rod of length 2M and mass M. Also the rod is exactly positioned where r = 2M. Furthermore if we decrease the length of the rod to the solution of a point mass, the solution is no longer spherically symmetric.

What, if anything, do you think is the significance of all this?

Fair question: Does the Schwarzschild solution refer to a removed rod or to a removed point mass?

Wait a minute, what do you mean by "Weyl form" here? And then how was the above image of the Newtonian potential in this "form" given?

AB

 

[Mentz114]

Do you have a reference I can look at ? One way of putting a Schwarzschild black hole into a Weyl vacuum is discussed in this paper, arXiv:gr-qc/0502062v1, but their [itex]\psi[/itex] ( equation 8) doesn't look like a Newtonian potential.

 

[Passionflower]

See for instance:

"Exact Space-Times in Einstein's General Relativity" - Jeremy Bransom Griffiths, Jiří Podolský
Cambridge University Press, 2009
Chapter 10.3, pages 178 and 179

http://books.google.com/books?id=Sb...od&pg=PA178#v=onepage&q=weyl form rod&f=false

 

[Bill_K]

This is a well-known result, but no, I don't think there's any significance to it.

 

[TrickyDicky]

The significance, if any is that since nothing can be physically a rod and a point at the same time that would make r=2m a physical singularity. So I would take Bill's advice and ignore it.

 

[Passionflower]

Ignoring things that can both be interesting and educational?

Looks like this forum is going downhill.