Another black hole question

I caught an episode of Through The Wormhole on black holes. Leonard Susskind talked about a hypothetical in which a pair of astronauts (Bob and Alice) fly near the event horizon of a black hole. Alice jumps in. To Alice, she perceives going in and ultimately being destroyed. What Bob sees is Alice slowing down as she gets closer and eventually seems to stop and will remain there indefinitely from Bob’s POV due to the extreme gravity’s distortion of space-time.

More here:

If this is true why don’t we see giant clusters of stars around the event horizon that have fallen into black holes as we view them with telescopes instead of nothing?

If spacetime distortion causes your perceived view of something to slow to a stop, by what means can you perceive it? Something frozen in time cannot reflect or emit light.

It sounds like your question proved them wrong.

In addition to what Mangetout said, black holes do not let any light escape, so at the point where Alice is supposed to “stop” from his reference point, light also stops reflecting back to him and thus there is nothing to see.

It sounds like this crap is made just to get ratings. Not based in reality. Like all the crap that formerly reputable channels like Discovery, History channel etc are putting out.

Mangetout has it, more or less. Suppose Alice’s ship has a laser beam on it that emits N photons per second with energy E each, and she shines it directly at Bob. As her ship approaches the event horizon, two things will happen: first, since a “second” on Alice’s ship takes a longer and longer time to elapse according to Bob, Bob will see the rate at which the photons get to him decrease with time; when Alice gets to the event horizon, the rate will go to zero. Second, the photons will get less and less energetic, since they have to “climb a hill” to get out from near the black hole. This means that the photons received by Bob will be less energetic than they were when they were emitted by Alice; this phenomenon is known as gravitational redshift. Again, the energy of the photons received by Bob goes to zero when Alice gets to the event horizon. In sum, as Alice falls in, the light she emits becomes dimmer (fewer photons) and less energetic, which for all practical purposes makes her impossible for Bob to see.

OK, then what does Bob see? Does Alice recede away from him then suddenly vanish?

Bob would see Alice slow down and freeze as the light she emits red shifts into infrared, microwave, perhaps even radio, until she crosses the event horizon. To Alice, she wouldn’t percieve anything strange happening at all crossing this point.

I’ve heard though, at this point, the information (all her atoms—everything she is and is comprised of) would be smeared across the two-dimensional sphere of the event horizon. A holographic projection effect of her 3-dimensional presence beyond the event horizon; Although Alice wouldn’t be aware of this at all.

There’s an hypothesis this might be how our universe really is, that all the information of everything within the universe is a 3D projection of a sphere, or event horizon, that embodies the universe; as if we were inside a black hole.

I’m prepare to be thoroughly corrected, however. winces

Also, keep in mind, black holes are usually very small, maybe a few miles in diameter. Any matter they suck in, is usually from itself, or a binary star creating an accretion disc as it siphons off the other star’s matter.

So, even if the light of atoms falling into the black hole didn’t red-shift, until it crossed the event horizon – ceasing radiation altogether – it’s not like you’d see objects just frozen and stuck into position all over it. The black hole’s gravity would actually completely disintegrate anything falling into it.

Alice would be stretched apart and atomized.

From his perspective, Alice just grows increasingly dim and red-shifted, and moves slower and slower. At some point before crossing the event horizon, she’ll be so dim that he can’t see her any more regardless of what kind of telescope or optics he uses - a gradual vanishing, if you will, rather than a sudden one. (If it helps, think about it like Alice going into deep water or dark fog. There’s no sharp cut-off, but a gradual dimming.) Bob will never see her hit the event horizon because there will be nothing to see.

Most of them are, but there’s no theoretical upper limit on how big a black hole can be, and a very large one such as those at the cores of galaxies would not necessarily spaghettify things falling into it (at least, not until after they’ve already crossed the horizon).

It’s not that her atoms would be spread out across the horizon, it’s just the information – in what form, though, nobody knows (you’d need a theory of quantum gravity that can describe a black hole’s microstates in order to answer this question; and while there are some candidates, such as the string-theoretic ‘fuzzball’ proposal, there’s really no consensus behind any of them).

Basically, the reasoning behind this is that a black hole’s entropy scales with its horizon area, rather than with its volume, and entropy can be regarded as a measure of how much information a system can store (essentially, entropy counts the number of microstates a system can be in, which gives you the amount of information you can store on it – a system that has only two possible microstates can store one bit of information, with four microstates, two bits (00, 01, 10, 11), and generally, for n microstates, log(n) bits of information; but the logarithm of the number of microstates is also just the system’s entropy, according to Boltzmann’s formula).

So, while you would naively expect the maximum amount of information within a certain volume of spacetime to be proportional to that volume (say there’s some elementary volume cell which can store one bit of information), that turns out not to be the case; rather, the information about this 3d-volume is proportional to the area of a 2d-surface, and can thus be imagined as being encoded there – that’s the ‘holographic’ aspect.