I am studying uniqueness theorems of Black Holes and I often see the word "regular event horizon" instead only event horizon. Many textbooks and literature do not define this term. Please explain what is the difference between event horizon and regular event horizon and what are regularity conditions that we assume in Israel's theorem?
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$\begingroup$ Often see where? Which page? $\endgroup$– Qmechanic ♦Commented May 3 at 12:58
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$\begingroup$ Four decades of Black Hole uniqueness theorems by D.C Robinson, page#2, first paragraph $\endgroup$– Talha AhmedCommented May 3 at 15:56
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$\begingroup$ See: arxiv.org/abs/1304.6592 (but for event horizon it refers to shape) $\endgroup$– WookieCommented May 4 at 7:59
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$\begingroup$ Regular is not a physical, but grammatical property meaning ordinary, typical, or not special. As opposed to what depends on the paper. It may be a different type like the Cauchy or Rindler horizon, photon surface (not the same as photon sphere), oddly shaped, and so on. $\endgroup$– safesphereCommented May 4 at 16:38
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$\begingroup$ @safesphere it could be grammatical, but my guess is here, it’s more mathematical, and based on context, I’m inclined to believe it refers to “being a level set of a regular-value of a smooth function” (i.e at every point in the level set, the smooth function has nonzero derivative). Or it could just mean being a smooth hypersurface (without the requirement of globally being a level set). I truly detest the use of the word ‘regular’ without further elaboration… $\endgroup$– peek-a-booCommented May 4 at 19:21
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