GR agrees (recognizing the obvious caveats) with the classical law of F = Gm₁m₂/r², where F stands for "force". This force is caused by spacetime curvature.
No, GR says that the Newtonian law of gravity is an approximation that makes reasonably accurate predictions when the spacetime curvature is small and all relative motions are slow compared to the speed of light. It does not say that the Newtonian interpretation of that equation is correct.
> GR says that the Newtonian law of gravity is an approximation that makes reasonably accurate predictions when the spacetime curvature is small and all relative motions are slow compared to the speed of light.
These are merely the aforementioned caveats.
> It does not say that the Newtonian interpretation of that equation is correct.
If the interpretation were wrong, and that's not a force, then the amount of force in that equation would be 0.
With no force, Gm₁m₂/r² = 0.
However, that's not the modification that GR applies to this, though.
> If the interpretation were wrong, and that's not a force, then the amount of force in that equation would be 0.
With no force, Gm₁m₂/r² = 0.
Nonsense. The GR interpretation is that G m1 m2 / r^2, when it is nonzero, is describing an effect of spacetime geometry, not a force. It can't be a force in GR because it isn't felt; an object moving solely under the influence of G m1 m2 / r^2 feels no weight--an accelerometer attached to it reads zero. GR does not change the numerical value of G m1 m2 / r^2 at all. It just reinterprets what the quantity represents.