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I was reading through this question on time and big bang, and @John Rennie's answer surprised me. In the immediate environment of a black hole, where does time stop ticking if one were to follow a 'watch' falling into a black hole?

  1. At the event horizon?

  2. In the central singularity?

If time stops at the event horizon, does the watch get stuck there, or does it keep falling in all the way to the singularity. Guess I know less than I thought.

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  • $\begingroup$ John wrote "It is often said that time stops at the central singularity in a black hole." - not the event horizon. Elsewhere John described what you feel when crossing the event horizon and What a remote observer sees $\endgroup$ – RedGrittyBrick Dec 31 '12 at 17:29
  • $\begingroup$ @mike I've answered, and I hope this clarifies things for you. Most of what I've said is covered by other questions already on the site, so there's a good chance the mods will close this as a duplicate. $\endgroup$ – John Rennie Dec 31 '12 at 18:47
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If you're sitting outside the event horizon watching a clock fall in, you will never see the clock reach the event horizon. You will see the clock slow as it approaches the horizon and you'll see it running slower and slower. However there is no sense in which time stops at the event horizon. You can wait as long as you want, and you'll see the clock creep closer and closer, but time will continue for both you and the clock.

Now suppose you're holding the clock. Assuming you can survive the tidal forces you'll cross the point where the external observer thinks the event horizon is (you would see no horizon there) and you would hit the singularity in a finite time. The problem is that at the singularity the spacetime curvature becomes infinite and there is no way to calculate your path in spacetime past this point. This is known as geodesic incompleteness (annoyingly Wikipedia has no good article on this but Google "geodesic incompleteness" for lots of info on the subject). It's because there is no way to calculate your trajectory past the singularity that it is said (but not by me!) that spacetime stops there.

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  • $\begingroup$ i hope its not closed as a duplicate, but lets wait and see. $\endgroup$ – mike Jan 1 '13 at 3:21
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I'm amazed people talk about crossing the event horizon. Time stops there. If you were to cross the event horizon and look out of the black hole you would only see the END OF THE UNIVERSE. Whatever its fate. Secondly a little discussed consequence is that space-time is curved in such a way that would take an object with mass infinite amount of time to move radially and require an infinite amount of energy. A photon would have to follow the curvature of space which is tangent at the event horizon. Also a photon is a travelling wave with electric and magnetic waves travelling perpendicluar to the direction of the photon. This energy can only propagate along spacial axis which doesn't have symmetric dimensions near the event horizon. So that in the space that is past the event horizon there is only TWO DIMENSIONS. I postulate you loose one space dimension and the time dimension. This is exacerbated if the black hole is spinning. Some neutron stars spin near .24c surface speed. So if a black hole spins near that speed the event horizon could be much faster. Include in this effect gravitational drag which is moving the compressed space in a circular motion. One last thing is the problem of quantum gravity(not in scope) with the INFORMATION LOSS when you cross the event horizon. This has a hyperthetically similar solution of the information or mass being smeared around the event horizon. A more important question is "why is a black hole a sphere not a spiral disk like most galaxies". This implies to me there are two dimensional forces at work. Gravity and maybe neutron degeneracy pressure. Galaxies and the rings of Saturn only have gravitational attraction and centrifugal force which act along the same axis. This all leads me to think that when a neutron star combines with another very large object and they convert to a black hole, the mass is extruded into a hollow sphere by a small black hole starting somewhere near the center and then growing and smearing the mass over the surface as a ever growing event horizon.

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    $\begingroup$ There are many mistakes here. If you were to cross and look out you would only see the END OF THE UNIVERSE. Whatever its fate. This is not true. See physics.stackexchange.com/questions/26185/… . Secondly a little discussed consequence is that space is constricted radially. Note true. General relativity doesn't describe gravity as a constriction of space, it describes it as a curvature of spacetime. $\endgroup$ – user4552 Dec 18 '19 at 1:23
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    $\begingroup$ One last thing is the problem of INFORMATION LOSS That would be about quantum gravity. The question is about classical gravity. Quantum mechanics is not relevant here. This all leads me to think that when a neutron star converts to a black hole Neutron stars don't convert themselves into black holes. $\endgroup$ – user4552 Dec 18 '19 at 1:24

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