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As seen here, gravitational acceleration as a Newtonian concept can be considered in General Relativity as an artifact of the selected frame of reference for measurements. But can one compute the same value that Newton's inverse square law would give from the mass of a considered massive body and a distance to said body, however using mathematical objects introduced by GR? I'm thinking about a Schwarzschild metric tensor that would be constructed with a given mass and distance. Is there an explicit way of computing gravitational acceleration relative to the massive body from such a tensor, and if there is, what is it?

Algorythmis
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  • Well if you’re talking about the schwarschild case then you can get the radial acceleration with respect to proper time for a massive particle for example. This video explains it: https://youtu.be/Z29Rfao92Zo And you can see it coincides with the newtonian limit in this case – Thatpotatoisaspy Jun 15 '19 at 03:26
  • @Algorythmis I see that this question is closed to answers, so I'll attach my own to some of the older similar questions. As a general comment, it's astonishing how many people put questions on this subject and how many answers have been written, with how many upvotes (I have seen one with 118). Yet I'm quite unsatisfied of most answers. In several cases they contain wrong statements - the most frequent, that spacetime curvature causes gravity. The best I can say is that it's a great oversimplification. – Elio Fabri Jun 16 '19 at 09:33
  • Another common statement is that bodies always move through spacetime - it's usually added that they move at $c$ speed. But I won't address those subjects in my answer - I prefer to stick to the title of the actual question and answer it in a rather easy way (but not in a popular way - it's impossible). IMO old John Rennies answer is too complicated and halts just where he should have started. The video quoted by Thatpotatoisaspy is a correct university level lecture, yet it too misses important points. When I'm finished writing my answer I'll put a notice here. – Elio Fabri Jun 16 '19 at 09:34
  • @ElioFabri any news? – Algorythmis Jun 01 '22 at 10:26

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