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?
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