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Assuming that no-hair theorem is correct, can the position of a massive body under the black hole's event horizon be communicated through the change in the space-time curvature gradient surrounding the black hole?

If the answer is "yes", isn't this conflicting with the statement that no information from under the horizon can be passed to the outside world?

Update: If the answer is “no”, does it mean that no-hair theorem is incorrect?

Eugene Dudnyk
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    One-word answers aren’t allowed, so I have to make it a comment: No. – G. Smith Aug 10 '20 at 22:35
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    I don’t see how your update makes sense. – G. Smith Aug 11 '20 at 00:27
  • You seem to be asking "is the impossible possible". – m4r35n357 Aug 11 '20 at 08:28
  • See https://physics.stackexchange.com/a/3204/123208 In particular, "rather than gravity having a special property that enables it to cross the horizon, in a certain sense gravity can't cross the horizon, and it is that very property that forces gravity outside of it to remain the same." – PM 2Ring Aug 11 '20 at 09:56
  • @PM2Ring I’ve seen other posts here on physics stack exchange about BHs, and someone claims there that gravity is scalar, so it does not cross the horizon, it’s “just there”. Still trying to make a sense of it, considering merging of BHs in real time, not in the infinite future. – Eugene Dudnyk Aug 11 '20 at 17:07
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    From http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html "If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole. [...] In this sense the black hole is a kind of "frozen star": the gravitational field is a fossil field". BH mergers are complicated because the initial BHs also contribute kinetic energy in addition to their mass, and a lot of energy gets radiated during the merger as gravitational waves. – PM 2Ring Aug 11 '20 at 17:40
  • The description I've most often seen is that, although the in-falling objects might remain faintly detectable (in principle) on the surface (or only infinitesimally far outside it) for whatever remains of the time during which all elementary particles (possibly excluding protons) on our side of the apparent horizon will decay, their actual detection would involve amounts of magnification energy exceeding that which appears to be accessible to us in our observable region. (I've noticed that the currently-unchallenged Wiki "No-hair theorem" has it down as a conjecture without rigorous proof.) – Edouard Dec 12 '20 at 17:44
  • @EugeneDudnyk --If gravity's scalar (so that it would be characterized by gravitons rather than spacetime curvature), there may be a problem, as scalar fields (whose value doesn't reach zero) don't rotate: Nearly all astronomically-detected black holes appear to have been formed by the gravitational collapse of stars, and virtually all stars are considered to have a least a faint residual rotation, even after whatever gravitational interactions they may've had with other stars. (What you're saying may apply to BH's formed by dust collapse, of which only one example's been detected.) – Edouard Dec 12 '20 at 18:09

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As the object closes in on the event horizon, its location gets smeared out all over the area of the event horizon. From our viewpoint, this takes an infinite amount of time but for practical purposes it means 1) the black hole's mass distribution remains spherically symmetric (no "lumps" in it that we could ever detect) and 2) as viewed from a safe distance away from the EH, anything that falls into it appears squashed into vanishing flatness just outside it and never "falls" all the way in.

niels nielsen
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  • "As the object closes in on the event horizon, its location gets smeared out all over the area of the event horizon." can you please elaborate on that? – Árpád Szendrei Aug 11 '20 at 04:46
  • I read that in another post about what happens when a concentrated mass approaches the EH. There is also a series of on-line videos put out by the black hole dynamics visualization and modeling research team headed by Kip Thorne that show this. I'll furnish the link if I can find it. – niels nielsen Aug 11 '20 at 06:33
  • The paradoxical thing about these sorts of issues is that, although the causal separation involved seems to me (a layperson) to have much more to do with time than with space, the time on the inboard side of the horizon seems to be passing more slowly (rather than more rapidly) than our own, even though space in the cosmological models based on them (-one can hardly avoid typing "crammed into them" instead) seem, in the English verbiage of such extremely accomplished physicists as Bojowald and Poplawski, to be tiny in comparison to the one to whose localities we have full and natural access. – Edouard Dec 12 '20 at 17:21
  • I'm obligated to upvote this answer as it's consistent with the impressions described in my comments. – Edouard Dec 12 '20 at 17:57