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Newton’s theory suggests it’s close to zero, but what says GR?

Edit 1: It’s obvious that at the center it’s zero for both theories. The curvature explanation of GR could give a different answer around the center. I mean expecting that curvature goes steeper around the center is more natural to me. Is this interpretation discussed before?

Edit 2: But why this interpretation?

Because of the pressure, things get denser. As density increases curvature gets steeper.

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