The metric was originally defined to be valid only from the surface of a black hole outward but somewhere along the line it was extended inward to include the region under the event horizon.

This extension of the metric was, of course, what gave us the definition of Schwarzschild black hole and I've been curious for some time about how the extension first came about and who did it.

  • $\begingroup$ @FrancoisZiegler … Thanks for the comments, Francois. I was familiar with the Wikipedia article but because of your link I read it again thinking I had missed something. Alas, I still couldn't find an answer to my question. Did I miss it, again? As for Eisenstaedt's papers, I couldn't get access to them, at least through the links provided. $\endgroup$ – dcgeorge Aug 3 '18 at 0:28
  • $\begingroup$ @FrancoisZiegler … OK, that seems to be getting closer to answering my question. It's too bad I haven't tried to translate from German to English in over forty years. Do you have a translation? $\endgroup$ – dcgeorge Aug 4 '18 at 0:38

The story is told in Eisenstaedt’s book (2006, Chap. 12) or papers (1982, 1987, 1989) (also jstor).

Briefly he says that, while Schwarzschild and Droste’s original works (1916, 1916, 1917) ignored the region $r\leqslant 2m$ (Schwarzschild actually used $\smash{\tilde r=(r^3-8m^3)^{1/3}}$ > 0 as his radial coordinate), other early papers like Hilbert (1917, p. 70), Eddington (1920, p. 97) or Lodge (1921, p. 555) did use the metric for all $r$ > 0. Putative crossing under the $r=2m$ “singularity” was also discussed at a 1922 Paris seminar of Einstein, as reported by Nordmann (1922, pp. 154-156) and Brillouin (1923).

The possibility was dismissed then, and apparently never seriously considered again until the early 1960s, when people discussed extended metrics. (Eisenstaedt also notes that Weyl had pioneered such an extension in (1917, p. 131; 1918, p. 205), but removed it from later editions of his book.)

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  • $\begingroup$ OK, so Hilbert extended it in 1917, not long after Schwarzschild came up with the solution. I should also have asked who first coined the term "Schwarzschild black hole". You wouldn't happen to know that would you? Anyway, thanks for the answer to my question, Francois, much appreciated. $\endgroup$ – dcgeorge Aug 8 '18 at 14:34
  • $\begingroup$ Probably Wheeler? He and R. Ruffini freely use it (as well as “Kerr black hole”) in proceedings of a 1969 conference (1971) and in Physics Today (1971, 2009). $\endgroup$ – Francois Ziegler Aug 9 '18 at 9:44

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