I Ricci Scalar For Astronomical Body

dsaun777
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What would be a rough estimate for the Ricci scalar curvature of an astronomical object like the sun? Assuming the sun is a perfect fluid and you are calculating the rest frame of the sun, only the density component would be factored in. Assuming the sun is roughly 2*1030 kg. Please just make very simplified assumptions, I am just looking for an estimate in terms of m-2. Is it just the Einstein gravity constant times the energy density?
 
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dsaun777 said:
What would be a rough estimate for the Ricci scalar curvature of an astronomical object like the sun?
There is no such thing as "the" Ricci scalar curvature for a large object. The Ricci scalar is a quantity at a particular event in spacetime, not a global quantity.

A rough estimate of the Ricci scalar at a particular point in a perfect fluid is ##(8 \pi G / c^4) ( \rho c^2 + 3 p )##, where ##\rho## is the density and ##p## is the pressure. So you can get a rough "average" value for a large body by using average values of ##\rho## and ##p##. For most bodies, like the Sun, ##p## is so small compared to ##\rho c^2## that it can be ignored. So an "average" estimate would be ##(8 \pi G / c^2) \rho_\text{average}##. The average density is ##M / (4 \pi R^3 / 3)##, so the "average" Ricci scalar would be ##6 G M / R^3 c^2##.
 
PeterDonis said:
The average density is ##M / (4 \pi R^3 / 3)##, so the "average" Ricci scalar would be ##6 G M / R^3 c^2##.
Yes, that is what I thought. Thanks.
 
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