I was wondering how stable a close star-black hole system could plausibly be, and thus how much time a star could plausibly miss out on (from an outside observer's perspective) due to being in an orbit at relativistic speeds around a black hole.
E.g. could there plausibly be a scenario where a star has only aged less than 13 billion years, but is in fact one of the universes's earliest Population II stars, because it has been in a fairly stable, close, rapid orbit around a black hole for the past few billion years*, and thus was subject to time dilation during a few billion years of orbits?
(*Or was orbiting a BH at some point, and escaped due to a chance interaction with a newcomer third body that tossed it out.)
Perhaps this would require a larger black hole, so that the tidal forces would be lower, which would presumably causing less gas stripping for an orbit that would result in the same time dilation? I realize that even well outside the photon sphere of a black hole, there can be decay of orbits due to gravity waves, but evidently there can be a counteracting separating phenomenon well, due to stars being stripped of some mass (e.g. as described in this report of a star orbiting a black hole at a velocity of about %1 of c).
So to put a number on this to make it more answerable, could a star plausibly orbit a black hole long enough and closely enough without spiralling in (or outward due to gas stripping) to make it half a billion years older in origin (according to the CMB rest frame) than it has experienced?