In Padmanabhan's Theoretical Astrophysics by defining a ratio for comparing gravitational potential energy with rest-mass energy it is shown that if massive objects with M=10^33 gm are confined to small regions with R= 1km then we cannot use Newtonian gravity because the system has general relativity effects.(adsbygoogle = window.adsbygoogle || []).push({});

I wonder if we do not use an energy ratio and instead use only Schwarzschild metric or Einstein field equations can we infer the same ratio between mass and radius?

I already see that Schwarzschild vacuum solution is asymptotically flat because the ratio of Schwarzschild radius over radius vanishes if the radius coordinate approaches infinity.

But establishing the above mentioned ratio of mass and radius for the threshold of general relativity without using the energy argument is not immediately clear.

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# The threshold of general relativity gravity

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