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I have been searching everywhere for the first order GR term that describes the gravitational force of a mass.

Could someone kindly show me the term that describes this?

Qmechanic
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1 Answers1

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Look up the term "precession of the perehelion of Mercury's orbit" in any general relativity text.

The term "gravitational force" is a thorny one in general relativity, and it does not map well to the formalism of the theory, but as mentioned in the comments, the Post-Newtonian expansion is the simplest way to apply that concept.