Do All Masses Exhibit Schwarzschild Singularities?

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SUMMARY

The discussion centers on the Schwarzschild solution in general relativity, specifically addressing the nature of singularities associated with mass. It is established that not all masses exhibit singularities; a singularity at r = 0 occurs only when a mass contracts within the r = 2M boundary, leading to black hole formation. The apparent singularity at r = 2M can be transformed away using a change of coordinates. For objects like Earth, the Schwarzschild metric accurately describes the gravitational field outside the mass, while the interior metric does not contain a singularity at r = 0.

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  • Understanding of general relativity concepts
  • Familiarity with the Schwarzschild solution
  • Knowledge of black hole formation criteria
  • Basic grasp of coordinate transformations in physics
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Physicists, astrophysicists, and students of general relativity seeking to deepen their understanding of singularities and the Schwarzschild solution.

supakorn
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From the Schwarzschild solution.This solution has two singularities,one at r = 0 and one at r = 2M.I have a questions
1.Every Mass has these singularities ?
2.For singularity at r = 0 it is the center of mass ?
thank you
 
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1. No mass has these singularities. If the mass were to contract inside the r=2M boundary, a black-hole is formed ( it is postulated), in which case there is a singularity at r=0. The apparent one at r=2M may be transformed away with a change of coordinates. In the case of the Earth, say, the actual radius is much greater than 2M and the Schwarzschild metric describes the field outside the matter.

2. The interior Schwarzschild metric describes the field inside the matter, and it does not have a singularity a r=0.
 

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