I would like to have a conceptually better understanding of GR solutions in the absence of matter, and a little difficulty I usually run into is that seemingly since in these solutions we have both the Einstein and stress-energy tensors equal to zero (which is what it means to have no matter-energy there) we are ignoring the curvature produced by any mass, however, when applying the solution to the Mercury precession problem or the bending of light by the sun problem, we are actually introducing the mass of the sun to solve them, and this to me seems a bit contradictory with the premise that there is no matter in the manifold under consideration.(adsbygoogle = window.adsbygoogle || []).push({});

Is there a simple way to explain away this false contradiction?

My own way to explain this is that actually in the Schwartzschild metric we have the expresion (1-2m/r) which seems to imply that we are substracting(that is close to ignoring) the curvature produced by the spherical symmetric mass from the total spacetime curvature, but I'm not sure if this is really so or even has any logic, it just helps me understand conceptually the premise of this vacuum solution.

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# GR Vacuum solutions

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