Metrics for the Sun & Earth: Rs & Assumptions

Philosophaie
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Is there a Metric for the Sun and Earth other than the Schwarzschild Metric who has the Schwarzschild Radius on the interior of the body?

What are the assumptions that turn that from GR to Newtonian?

Rs(Earth)=8.87*10^-3m
Rs(Sun)=2954m
 
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The Schwarzschild radius is outside the body pretty much by definition... though you can see where the Schwarzschild radius would be if all the matter were concentrated at the center ... but that is always inside the body for objects less massive than black holes. So I think you need to be a bit more precise about what you mean.

It is probably possible to produce a metric which has a coordinate singularity anywhere you like.
 
Philosophaie said:
Is there a Metric for the Sun and Earth other than the Schwarzschild Metric who has the Schwarzschild Radius on the interior of the body?

What are the assumptions that turn that from GR to Newtonian?

Rs(Earth)=8.87*10^-3m
Rs(Sun)=2954m
As you point out, the Schwarzschild radii for the Earth and Sun are inside the physical bodies. But that is not a problem because the exterior Schwarzschild solution applies to any spherically symmetric static( stationary?) spacetime.

If the spatial curvature is ignored and all velocities << c, and r>>m one can recover the Newtonian equations.
 
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