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Inspired by outdated concepts in special relativity such as When and why did the concept of relativistic mass become outdated? and Special relativity and imaginary coefficient of the time coordinate, are there any outdated concepts in general relativity?

To be specific, I am looking for mathematical entities in general relativity that are mathematically sound like relativistic mass and use Euclidian metric with time $t\to it$ to get Minkowski metric in special relativity (see links above), but that are no longer described as such, have been superseded by a better interpretation, or that many physicists have argued against the utility of such a concept.

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  • $\begingroup$ Does "outdated" mean 'necessary but currently unfashionable' or 'unnecessary, mistaken or obsolete'? e.g. the concept of relativistic (inertial) mass is 'necessary but currently unfashionable'. Studying 'necessary, but currently unfashionable' is not a study of history, but of current intellectual biases and preferences. $\endgroup$
    – James Arathoon
    Mar 29 at 16:55
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    $\begingroup$ @JamesArathoon outdated as in part of the theory but it is no longer a custom to define it that way anymore for pedagogical reasons. I would disagree that it is not historically interesting as seen from the links above there can be clear examples. Many old books did introduce special relativity using relativistic mass and Euclidian geometry with imaginary time. From a moment on we decided to not introduce those concepts anymore and there were academic conflicts about it. $\endgroup$
    – Mauricio
    Mar 29 at 19:21
  • $\begingroup$ The Sagnac Effect has always been omitted from undergraduate and graduate texts on Special Relativity and General Relativity. The experimental result has never been disputed and is used by engineers as the basis of light based gyroscopic stabilisation techniques. Should the Sagnac effect be described in university texts on Special Relativity or General Relativity even though it does not fit in with the standard pedagogy of either. $\endgroup$
    – James Arathoon
    Mar 30 at 14:02
  • $\begingroup$ @JamesArathoon did not know about it, what is controversial about the Sagnac effect then? $\endgroup$
    – Mauricio
    Mar 30 at 15:41
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    $\begingroup$ One example in GR is the idea of "central singularity" in the Schwarzschild solution. Krasnikov says (p.4) that it "goes back to classics of the pre-Kruskal epoch and is amazingly widespread even today" and "though not wrong... is, nevertheless, grossly misleading". He discusses a couple of other misconceptions, but I am not sure if they fit your criteria. $\endgroup$
    – Conifold
    Mar 31 at 11:11

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