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A well-known (but usually only cursorily discussed) feature of General Relativity is the so-called radial (or volume) excess due to the curvature of spacetime in the presence of mass/energy (or more properly the effect of mass/energy on the Ricci curvature). See for instance Chapter 42 of the second volume of the Feynman Lectures, where the radial excess of the earth is estimate to be about 1.5mm: http://www.feynmanlectures.caltech.edu/II_42.html.

When was this first explicitly recognised, and by whom? I am specifically interested in the occurrence of the relevant equations in the literature, and numerical estimates of the magnitude of the effect for e.g. the earth. References welcome.

To be clear, my question is specifically about General Relativity, and answers should therefore refer to material after 1915.

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  • $\begingroup$ This is my first post on this site. I see my question has not attracted much attention. I am happy to improve the question if anyone has suggestions in that regard. $\endgroup$ – Martin C. Nov 16 '18 at 18:35
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    $\begingroup$ I don't know the actual answer Martin, but Einstein did talk about this in The Foundation of the General Theory of Relativity. Note that the Feynman lecture confuses curved spacetime with curved space. Space isn't curved where a gravitation field is, instead it's neither homogeneous nor isotropic, in a non-linear fashion. $\endgroup$ – John Duffield Nov 19 '18 at 21:24
  • $\begingroup$ @JohnDuffield Thank you for the comment and the reference. I will be sure to check it out. $\endgroup$ – Martin C. Nov 20 '18 at 7:12

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