Undergrad Spherically Symmetric Metric: Is Singularity Free?

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SUMMARY

The discussion centers on the existence of spherically symmetric metrics without singularities, specifically contrasting them with the Schwarzschild metric. The interior Schwarzschild solution, FLRW (Friedmann-Lemaître-Robertson-Walker), and flat spacetime are identified as metrics that do not exhibit singularities at their centers. Additionally, the Oppenheimer-Snyder model is mentioned, which begins without a singularity but develops one over time. The conversation also touches on the relationship between Newtonian gravity and general relativity (GR).

PREREQUISITES
  • Understanding of general relativity (GR)
  • Familiarity with spherically symmetric metrics
  • Knowledge of the Schwarzschild solution
  • Basic concepts of cosmology, particularly FLRW models
NEXT STEPS
  • Research the interior Schwarzschild solution in detail
  • Explore the FLRW metric and its implications in cosmology
  • Study the Oppenheimer-Snyder model and its evolution
  • Examine the Tolman-Oppenheimer-Volkoff equation and its significance in GR
USEFUL FOR

Physicists, mathematicians, and students of general relativity interested in understanding spherically symmetric metrics and their implications in gravitational theory.

sqljunkey
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Is there a spherically symmetric metric that doesn't have a singularity in the middle of it(like the schwartzchild metric). Something like our planet.
 
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sqljunkey said:
Is there a spherically symmetric metric that doesn't have a singularity in the middle of it(like the schwartzchild metric). Something like our planet.
Sure. That is the interior Schwarzschild solution. There is also FLRW. Also flat spacetime. And Oppenheimer-Snyder which starts out with no singularity but develops one later.
 
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sqljunkey said:
Something like our planet.

Newton's gravity force is proportional to distance from the center up to the Earth surface and dumps inverse square of distance outward. Together with OP I am interested in the corresponding formula in GR.
 

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