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I think black holes don't actually have a diameter of zero. It's only a mathematical convenience to make that claim based on the fact that light cannot escape and therefore any real diameter can be ignored.
I propose that stars or other massive objects be run past black holes at very, very high speeds,
just far enough away to be at escape velocity. Do it enough and you'll increase the spin of the black hole to a point that it can't hold itself together anymore. At this point it will no longer be a black hole and you'll be able to learn what its diameter was.
The Bet
http://www.theory.c.../new_naked_bet.html
Hawking wants this answered, too [lurch, Oct 12 2011]
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Ignoring the comment on escape velocity re:tidal effects,
how would breaking apart a black hole tell you its
diameter? By definition the matter in a hole is
gravitationally compressed, breaking it apart will reduce or
eliminate that compression. |
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This is great apart from the science bit. |
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How can you tell the diameter of something that has no
substance after every trace of it is gone? Won't slinging a
bunch of mass past the black hole alter its theoretical
dimensions in the first place? If I dig a large hole around a
smaller hole to get rid of it, then fill the second hole in
with a backhoe, build a Wally-Mart over where it was,
then drop a tactical nuke on it, I doubt I'll be able to
determine the diameter of the original hole. |
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//It's only a mathematical convenience// ... based on the fact that any space that the black hole may be occupying has been pulled in after itself. The black hole may, indeed, occupy space - but if it does, the space is outside our observable spacetime. |
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Actually, a black hole with any angular momentum will expand into a torus, with a non-zero radius, but still occupying zero volume - at least, on our side of the singularity. Anything beyond, we don't know what the rules are; so we can't even rationally talk about it. Fantasize, yes; theorize, unsupportedly; determine, no. |
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You should email this to Prof. Stephen ("We Are Not Worthy !") Hawking. He could probably do with a good laugh. |
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Hawking seems to think that the entire mass of a black hole can radiate away in a (yet to be detected) form of radiation which somehow exceeds the escape velocity of the hole to begin with. I prefer to think of the black hole as an actual hole, through which *stuff* falls and then ceases to exist in our universe. You could probably impart spin to a black hole by flying past it really quickly, but it would not unravel. |
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I for one would be interested in seeing what the effects would be. Not even black holes can have infinite gravitation, right? Or does that even matter? |
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If you know something about the amount of mass / inertia you're sending past it, and you record the point at which it starts to break apart, then you would know something about it's mass and potentially therefore its diameter? |
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// an actual hole, through which *stuff* falls and then ceases to exist in our universe. // |
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It's called "Your Wife's Collection Of Shoes, Dresses, and Jewellry". |
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// You could probably impart spin to a black hole by flying past it really quickly, but it would not unravel // |
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Hence the term "Drive-By Spooling". |
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// Not even black holes can have infinite gravitation // |
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It doesn't need "infinite" gravitation. It just needs its gravity to be sufficient that its escape velocity is >= C. Once that point is passed, it's just adding more gold leaf to the dog turd. |
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Reminds me of the blackholeapult discussion awhile back. |
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The one where you could carry almost unlimited ammunition because it was so light ? ... point being that it would pick up mass on the way to the target. |
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If the acceleration of gravity towards a black hole is >c, can an object flying into a black hole at nearly c exceed the speed of light? Hmm. I'm going to a lecture on space-time tonight, hopefully I'll learn the answer. |
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The falling matter may exceed the speed of light once inside the Schwarzchild radius in which case it goes to a when. |
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"This is great apart from the science bit" |
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[Voice] and [DIYMatt], you need a few more facts. First, the diameter of a black hole is NOT the same thing as the diameter of its mass. So, while the diameter of its mass can be zero; the diameter of the overall "hole" it a rather larger and mathematically defined region inside of which the escape velocity is greater than light-speed. |
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So, if a neutron star collapses into a black hole, the diameter of the object-as-an-object actually only shrinks a little (the escape velocity from the surface of a neutron star is typically already about 60% of light-speed). That mathematically defined "surface" of a black hole, at which the escape velocity is exactly light-speed, is called "the event horizon". |
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Next, the mechanism proposed by Stephen Hawking, by which a black hole can lose mass, is a phenomenon of Quantum Mechanics that happens AT the event horizon. It involves "virtual particles" that are able to temporarily spontaneously appear ANYWHERE and at any time (and which normally vanish again, after their temporary existence is over-and-done-with). |
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It is the well-verified Uncertainty Principle of Quantum Mechanics that allows virtual particles to BORROW some energy from Nothingness, in order to do their temporary-existence thing. Unlike the banking industry, they don't have to pay back "interest" on the energy they borrow, but they do have to sacrifice their own existence to pay the "principal" back. |
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Physicists are quite sure that virtual particles exist (look up something known as the "Casimir experiment"), and it happens that those particles almost always pop into existence in pairs --and must vanish in pairs (because of various Conservation Laws). Also, virtual particles are allowed to possess any speed up to very nearly the speed of light, when they first pop into existence. |
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So, JUST outside the event horizon of a black hole, if a virtual pair begins to exist such that one particle moves away from the hole while the other moves toward it, the one that moves away can escape the black hole, while the other cannot. They also cannot recombine to vanish again! So, the particle that escapes becomes "real", no longer "virtual", but it can do so only if the "principal" energy of its existence is "paid" for, somehow. The black hole does the paying, by losing an appropriately teensy bit of mass. |
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It is important to note that there is no "faster than light" weirdness involved. |
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Finally, regarding this Idea, I think the most that would happen is that the black hole would eventually assume a doughnut shape. Such a shape has actually already been studied by astrophysicists, and has some interesting properties. But the black hole would not be destroyed by such a shape-change.... |
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//Actually, a black hole with any angular momentum will expand into a torus// [lurch] |
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//I think the most that would happen is that the black hole would eventually assume a doughnut shape.// [Vernon] |
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Really? A torus rather than a disc (more correctly an oblate spheroid)?
Why's that? |
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//It is important to note that there is no "faster than light" weirdness involved.// |
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How is it possible to know this? |
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Exactly! One of the only things we know for certain (to a
given
degree of 'certainty' as yet another variable) about black
holes is that, in [Alterother] terms, light goes in and
doesn't come back. If that's the case, how can anything
going _slower_ than light have a dramatic enough effect
on a black hole to 'destroy' it? I'm even arrogant enough to
assume that Dr. Hawking might agree with that, albeit in
the form of correction. |
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Not that I really belong in this argument... |
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//You should email this to Prof. Stephen Hawking.// |
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He has already considered it. (Unsurprising, I think...) Look up stuff about "cosmic censorship", or "the cosmic censorship principle". |
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First off, you have to remember that the "event horizon" and the "singularity" are not the same thing. In the usual situation, the singularity is hidden inside the event horizon - so you can never see the shape of the singularity. (This is the "diameter of the mass" thing that [Vernon] mentioned.) |
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[Voice]'s idea would increase the angular momentum contained within the singularity to the point that its radius would be larger than that of the event horizon. Thus it would be exposed to the universe as a "naked singularity" - but Hawking believes cosmic censorship would save us from said embarassment. Preskill and Thorne believe otherwise, hence the bet. |
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//A torus rather than a disc (more correctly an oblate spheroid)?// Again, I'm guilty of conflating terms. The event horizon (the Schwarzchild metric), the set of points around the singularity where the escape velocity equals the speed of light, does indeed remain as a spheroid; oblate if there is angular momentum contained in the singularity (Kerr metric). The actual singularity inside the event horizon undergoes total collapse to zero-volume degenerate forms. |
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But, since angular momentum is determined by mass, rotational speed, and *radius*, a zero-radius singularity would need to have infinite rotational velocity - no, the equations just blow up. It has a radius. But still nothing else; it has zero volume. |
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Likewise, it would take infinite force to compress a finite charge into a zero radius - therefore a singularity with charge expands to a surface, but still zero volume. |
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Charged black holes, while mathematically workable (Kerr-Newman and Reissner-Nordstrom metrics), are mathematical constructs which rely on the cosmological constant being zero. That is no longer believed to be the case, so the current theoretical treatment for charged black holes is not well grounded. Besides, we don't have much evidence for bulk astronomical objects being electrically non-neutral, so it is really just a play-with-figures exercise which may not describe any real physical thing. |
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Kudos to Voice, then for stumbling into something that Hawking, Preskill, and Thorne disagree about. |
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Like [Alterother] said I don't really belong in this argument either I just can't help wondering... out loud. |
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//But, since angular momentum is determined by mass, rotational speed, and *radius*, a zero-radius singularity would need to have infinite rotational velocity - no, the equations just blow up. It has a radius. But still nothing else; it has zero volume.// |
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What if the equations blow up because it is insisted that the matter remain present within the singularity without exceeding the speed of light?
Also, if spun fast enough then wouldn't the oblate spheroid become piriforme? and if so, could part of it ever break away? |
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Theoretically, there is a maximum angular momentum for a BH --Jmax < M2G/c |
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Before we smash the black hole into tiny itsy bits, can we first toss in all our garbage and medical waste and all the old National Geographics (or at least the ones that don't show any good bits) and Yugo's and vuvzelas and sushi and clown hair wigs? [+] Regardless. |
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The term "diameter of a black hole" actually has very little meaning, because you first need to define the hole's "edges" to carry out a measurement. How do you make that a fixed definition? You may as well try and measure the diameter of a whirl-pool vortex. |
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People asked me if I was OK. Questioning the same. Not as
soundly, did I as you, though. + |
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