Schwarzschild and Newton potential

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Discussion Overview

The discussion revolves around the relationship between the Schwarzschild solution in general relativity and the Newton potential, particularly in the context of expressing the Schwarzschild solution in Weyl form. Participants explore the implications of representing the Schwarzschild solution as a rod of length 2M and mass M, and the transition to a point mass, questioning the significance of these representations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that expressing the Schwarzschild solution in Weyl form allows for the use of the Newton potential, which they suggest is equivalent to a rod of length 2M and mass M positioned at r = 2M.
  • Others question the meaning of "Weyl form" and seek clarification on how the Newtonian potential is represented in this context.
  • One participant references a paper discussing the incorporation of a Schwarzschild black hole into a Weyl vacuum, noting that the equations presented do not resemble a Newtonian potential.
  • Another participant cites a book as a reference for further reading on the topic.
  • Some participants express skepticism about the significance of the results, with one stating that there may be no importance to the relationship between the rod and point mass representations.
  • Another participant argues that the duality of being both a rod and a point mass at r=2M implies a physical singularity, suggesting that this should not be ignored.
  • A later reply critiques the dismissal of potentially interesting and educational aspects of the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the significance of the relationship between the Schwarzschild solution and the Newton potential. Multiple competing views remain regarding the implications of representing the Schwarzschild solution as a rod versus a point mass.

Contextual Notes

There are unresolved questions regarding the definitions and implications of the Weyl form and the nature of the Schwarzschild solution as it relates to physical singularities.

Passionflower
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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?
 
Last edited:
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Passionflower said:
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
 
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.
 
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This is a well-known result, but no, I don't think there's any significance to it.
 
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.
 
Ignoring things that can both be interesting and educational?

Looks like this forum is going downhill.
 

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