Spherically Symmetric Metric: Is Singularity Free?

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Discussion Overview

The discussion centers on the existence of spherically symmetric metrics that do not exhibit singularities, particularly in the context of general relativity. Participants explore various solutions and models that may represent such metrics, drawing comparisons to physical objects like planets.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether a spherically symmetric metric can exist without a singularity, referencing the Schwarzschild metric as an example.
  • Another participant suggests that the interior Schwarzschild solution, FLRW, flat spacetime, and Oppenheimer-Snyder models may provide examples of spherically symmetric metrics without singularities, although the latter develops a singularity over time.
  • A separate post mentions the Tolman–Oppenheimer–Volkoff equation as a relevant reference for the discussion.
  • Another participant expresses interest in the gravitational force in relation to distance from the center of a planet, seeking a corresponding formula in general relativity.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence of singularity-free spherically symmetric metrics, as multiple models are proposed and some participants express differing views on the implications of these models.

Contextual Notes

The discussion includes assumptions about the nature of singularities and the applicability of various metrics, which may depend on specific conditions or definitions in general relativity.

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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