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СпутникиРНSpaceXРоскосмосNASAI think, as is usually the case, if you have a fairly middle-of-the-road case like a planet then Newton is sufficient and mathematically much simpler. Why bother including the contribution of pressure and internal energy to gravity when it's a correction on the fifteenth decimal place, or whatever?
Binding energy is certainly a concept in GR - if two distant objects fall together under their mutual gravity and collide plastically the kinetic energy converted to heat in the impact is calculable (in principle!). And the energy you need to supply to separate them to infinity again is well defined. It just doesn't have an interpretation in terms of released GPE.
Thank you.
In general you specify a material model in the form of differential equations relating the components of the stress-energy tensor, and initial conditions that describe your specific scenario. This is exactly the same input as Newtonian physics. My example is just very simple, with unvarying material properties so there's no clear distinction between initial conditions and the material model.
Cosmological models, for instance, relate the density to the scale factor as ##\rho\propto a^{-n}##, where ##n## depends on the type of stuff (##n=3## for matter, ##n=4## for radiation, for example) and relate density to pressure by ##\rho=wp##, where ##w## again depends on your type of stuff. The resulting system of equations is soluble analytically for "pure" cases, but more realistic cases with a mix of matter and radiation and dark energy requires you to resort to a numerical integrator.
Of course. The same is true in Newtonian gravity. Why do you express this as an objection?
Newtonian gravity doesn’t work in the strong field regime.
You are trying to claim some superiority of Newtonian gravity over GR, so your objections here make no sense. They are either things that are the same with Newtonian gravity or things where Newtonian gravity fails.
About the only things that actually is better for Newtonian gravity is that its equations are simpler to calculate. Everywhere that Newtonian gravity makes accurate predictions, so does GR. You can take the same inputs, plug them in to GR’s more complicated equations, and get the same output. But the reverse is not true. In many cases GR makes accurate predictions but Newtonian gravity does not.
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