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Could someone please show using equations if space-time curvature due to two bodies being linearly additive or not in general.

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To see in a very concrete case that it is not additive, consider two spherically symmetric bodies centered at the same point. If you don't like them to overlap, take a ball and a spherical shell that doesn't intersect. Then at sufficient distance we have (wikipedia) that

$$R^{t}{}_{rrt} = \frac{r_s}{r^2(r_s-r)}$$

Since $r_s$ is linear in the masses, the curvature isn't.

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