At the time Schwarzschild derived his solution (1915) he only had a version of the EFE that was not fully coordinate free, he used the equations in unimodular form, and therefore he could only consider the "outside of the star" part of the fully general covariant form we know now.(adsbygoogle = window.adsbygoogle || []).push({});

So does a "local" approximation of GR always imply loss of general covariance?

I guess that as long as we impose the coordinate asymptotic flatness condition to derive the metric (like is done in the usual textbook Schwarzschild metric derivation) the answer is affirmative.

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# Schwarzschild's solution, classical (local) GR tests and general covariance

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