Hello. Let me start off by saying that I am new here and that I am not actually a physics major. Still, this stuff interests me. So, I was watching this clip of that good ol' documentary about Stephen Hawking, And when Hawking was talking about how the image of something falling into a black hole would slow down from the perspective of an outside observer, and how, from the perspective of the infalling object, the rest of the world would speed up infinitely, I became confused about how the particle could ever actually get around to falling into the black hole. I was pleased to find that my questions were not new: http://www.wired.com/wiredscience/2007/06/black-holes-don/ http://blogs.discovermagazine.com/badastronomy/2007/06/19/news-do-black-holes-really-exist/ So, this is not meant to be a post about some personal theory or anything, but I just can't figure out why the following scenario wouldn't be the case: Because of time dilation, an outside observer never actually witnesses the black hole forming. The witness sees matter collapsing into itself and asymptotically approaching, but never quite arriving at, the certain critical density at which the event horizon would form. But the observer never actually witnesses the event horizon form. From the perspective of the person falling along with the self-condensing matter and approaching the formation of a black hole, time goes on at the same normal rate locally, but still the person or particle will never get around to experiencing the formation of an event horizon or black hole because the observed time of stuff outside of the condensing black hole will speed up infinitely. The rest of the universe, then, will end in that last second before the particle ever quite makes it to forming an event horizon (or rather, time in the outside universe will appear to pass more and more quickly towards infinity as that 1 second elapses for the innermost particle). So even if there is no end to the universe, there's no problem. In any case the black hole would eventually evaporate, right? Even without Hawking radiation, wouldn't the black hole eventually evaporate just from quantum tunneling? Consider: An innermost particle of the condensing ball of matter is 1 picosecond away from forming a black hole. As that innermost particle gets closer and closer to forming a black hole, and as spacetime gets more and more sharply warped towards forming an event horizon (but not quite doing so), the outside universe will appear to accelerate infinitely. First, at 0.9 picoseconds until event horizon formation, the innermost particle will witness particles at a distance of, let's say, 1 meter outwards, accelerate in time towards infinite rate of time (as the spacetime within that 1 meter span approaches infinite, singularity-like warping (but not quite reaching that). Although the probability is extremely low that the particle at 1 meter's distance will escape the gravity well of the massive ball of matter and quantum tunnel out of the entire collapsing ball of matter, that probability is still nonzero. Furthermore, as time for this 1m distant particle appears to accelerate infinitely from the perspective of the innermost particle, that innermost particle will witness the 1m distant particle as having a number of "chances" to quantum tunnel out of the gravity-well that approaches infinity. It then becomes a certainty that the innermost particle will witness the 1m distant particle being ejected from the gravity well before those 0.9 picoseconds have elapsed for the innermost particle. Let's go down to 0.00001 picoseconds left until the innermost particle gets compressed to the density necessary to form an event horizon. At this point, spacetime becomes so locally warped that even a particle 0.00001 picometers further outwards from the center will be perceived as having its time accelerate to infinity. From the perspective of the innermost particle, the .00001 picometer distant particle gets a number of chances to quantum-tunnel out of the gravity-well that approaches infinity. That 0.0001 picometer distant particle, from the perspective of the innermost particle, eventually does escape as well. Now all that's left of the condensing ball of matter (the formerly soon-to-be black hole) is that innermost particle. The density required to form a black hole is no longer there, so spacetime goes back to its "normal" level of gentle warping, and time in the rest of the universe goes back to a more "normal" pace, and that innermost particle never gets to experience the formation of an event horizon or black hole, even though at one point it got asymptotically-close to doing so before the rest of the layers around it accelerated in time towards infinity and evaporated away due to a nearly-infinite number of quantum tunneling chances. And all of this condensation and evaporation took place in the span of 1 second, from that innermost particle's perspective. Meanwhile, the rest of the outside universe has aged millions, perhaps billions, perhaps trillions, perhaps quadrillions of years (however long it takes a black hole to evaporate through quantum tunneling). What this would mean for physics is that we no longer have to worry about what the universe or spacetime is like at a singularity, because singularities never get a chance to form (even though we might spot things in the universe with our telescopes that have a gravitational signature that is asymptotically-similar to singularities). There is never an escape velocity anywhere in the universe that is greater than the speed of light, and there is never any lost information or information paradox. I don't understand, why would this not work? Thanks for any feedback!
The gravitational time dilation at the event horizon is only infinite for an observer at infinite distance. This is rather a theoretical point since he cannot observe anything due to infinite light travel time anyway, black hole or not.
I'm sure that's not right. It's partly a matter of choice of coordinate system, but I think it's probably infinite for almost all observers, certainly including any at rest or with a constant velocity relative to the black hole.
Matthew: I would suggest that you take a look at the Usenet Physics FAQ article on "what happens to you if you fall into a black hole." It gives a good description of how the physics works, and explains why things don't work the way you were thinking they might. Regarding the links you gave, they don't appear to link to the actual paper they talk about, or quote from it (which is always a bad sign). I'll see if I can find a copy of it on arxiv.org. From reading the articles, I strongly suspect that either the writers of the articles have misinterpreted something the writers of the paper said, or the writers of the paper themselves don't understand general relativity. (They wouldn't be the first--plenty of papers have been written, and some even published, making the error I suspect these writers are making.) One of the other regulars here may already have seen the paper and can comment with more knowledge.
Nobody ever sees a black hole form. Nobody ever sees the singularity at it's center. The event horizon obscures all that. Only light observed from within the critical circumference continues to be observable....light ceases to exist outside it. Kip Thorne (Black Holes and Time Warps) page 133 explains Hawking radiation can be thought of as quantum tunneling. Another way to think about Hawking radiation is that a free falling observer sees virtual particle pairs and is unaffected; a stationary observer hovering outside the event horizon sees only REAL particles and is radiated/vaporized etc. Near the horizon the separation into thermal and quantum depends on the observer. Since black holes have a temperature, which Bill Unruh proved as well as Hawking, they emit black body radiation, another way of thinking about what's happening. . Wikipedia claims Hawking radiation can also be explained by the Unruh effect: http://en.wikipedia.org/wiki/Hawking_radiation#Emission_process And Leonard Susskind likes to explain black holes in terms of information and entropy(THE BLACK HOLE WAR,)...so there are lots of viewpoints...I'm not expert enough to decipher the fine points of difference and strengths and weaknesses of the alternatives... As far as is known, all astronomical black holes are actually growing, not evaporating....even the most isolated black hole is sourounded by heat...the cosmic microwave background radiation...and is absorbing it.... But as you suggest, they will eventually evaporate assuming they really exist in the first place. I stopped skimming the blog for Discover magazine when I saw: "But you know this. Infinitely small, with huge gravity, warpers of time and space; .." guess nobody told them the supermassive balck hole at the center of the Milky Way (our galaxy) is about 100,000 miles in diameter....maybe they meant the singularity...
For observers hovering at rest relative to the hole (and accelerating to do so), the time dilation factor goes to infinity as their radial coordinate r approaches the horizon at r = 2M. For observers freely falling into the hole, however, it does not. They reach the horizon in a finite proper time by their own clock, even though the Schwarzschild coordinate time t at the horizon is infinity. As such observers fall past accelerating observers hovering at rest relative to the hole, they will find that those observers' clocks are running slow relative to their own, by a factor similar to the time dilation factor comparing the hovering observers' clock rates to clock rates very far away from the hole.
Hey everyone! Thanks for all of the speedy replies! So, I took a look at the FAQ on "What happens to you if you fall into a black hole," and I was surprised to find this: So if this is true, then I can see how this would invalidate my earlier thoughts. Instead of witnessing an approachingly-infinite amount of time pass by in the outside world during my 1 second of plunging towards an event horizon formation point, I only see a finite amount of time in the outside world pass---not enough time to allow the universe to undo the conditions for forming the black hole in the first place (regardless of whatever mechanism would accomplish this, whether quantum tunneling or Hawking radiation or whatnot). By the way, how would one calculate how much time this finite speed up of the observed outside world would be? Also, I can also see how, even if black holes did work like I originally was thinking, with the infinite speed-up in the outside world, you'd still get some (different) crazy results: If approachingly-infinite time were to pass in the outside world, then the energy coming in would be approachingly-infinitely blue-shifted, and would have approachingly-infinite energy, and so one's rapidly-forming black hole would never really get a chance to evaporate, but would constantly be growing bigger and bigger, until it had gobbled up all other light and matter in its light-cone (including other black holes) and basically ended the universe, (all of this in 1 second, from the perspective of the infalling person, and all of this without an event horizon ever technically being formed, but rather just a constantly-enlarging*** spherical surface layer of asymptotically-condensing matter, right on the cusp of forming an event horizon (but from the outside perspective, never quite getting there). ***Edit: That is, constantly-enlarging from the outside perspective (as more of the space-time grid got pulled in), but still collapsing from the perspective of the person falling in for that 1 second). If this were the case, then I guess we'd observe the universe end in a bunch of "mini-crunches," with a bunch of black holes remaining as all that would be left. Those black holes would then drift away from each other towards infinity, if the universe were open, or then themselves crunch together into bigger crunches if the universe were closed...and then maybe eventually the black holes could get around to evaporating, but only after the rest of the universe had been made completely dark...and still all of this would take place in 1 second from the perspective of the infalling person, unless, as that first quoted paragraph up above asserts, an infalling person does not see time speed up infinitely outside. But I'm still unclear about why that would be.
Ah, I found another FAQ that explained things in more detail: http://www.phys.vt.edu/~jhs/faq/blackholes.html#q11 Okay, that makes sense. Still, though, would one be correct in saying that, from our reference frame on Earth, no black holes have ever formed in "the" (our) universe? Sure, we can say that black holes exist in other frames of reference (such as the frames of reference of those particles that have fallen in), but would one be correct in asserting that, from the Earth's frame of reference, no black holes yet exist in the universe (only matter densities that are continually, from our frame of reference, on the verge of forming event horizons and black holes), and that this will continue to be the case, until the Earth actually does go into a black hole, in which case we really could say that, from the Earth's reference frame, "the" (our) universe has at least that black hole? Also, a slightly related question on Hawking radiation: if a virtual particle/anti-particle pair comes into existence, and one goes into the black hole, and the other one shoots off into space, how is it not the case that the black hole has just become a little more massive, and that the universe has also just become a little more massive? Must a previously-existing particle/anti-particle pair somewhere else suddenly snap out of existence to maintain the balance of matter/energy in the universe? Is half of this other pair within the black hole, and half in the rest of the universe? (Because if both parts of this other pair that disappears were in the outside universe, then the net effect would be for the universe to get less massive and for the black hole to get more massive. And vice-versa if both parts of this other pair were within the black hole).
In curved spacetime, there is no global notion of "when" events happen. Any notion of "when" things happen can only be local. Our notion of "when" things happen here on Earth is fine for our local region, but it has no meaning when applied to events near a black hole's horizon; the curvature of spacetime in between prevents us from extending our notion of time that far. One way to think of it is that the particle that drops into the hole has negative energy, so it makes the hole's mass smaller, not larger. If that doesn't quite make sense, here's another way to think of it. Normally, when virtual particle-antiparticle pairs form, they have to temporarily "borrow" energy from the vacuum to do so; but this borrowed energy can only last as long as the uncertainty principle allows. In flat spacetime, that means the pair ends up annihilating each other a very short time after they form. But the tidal gravity near the hole's horizon pulls the pair apart before they can annihilate each other; in the process of doing that, the particle that shoots out into space "borrows" enough energy from the gravitational field of the hole to become a real, positive-energy particle. But that energy has to come from somewhere: in fact, it comes from the hole's mass, making it a tiny bit smaller (which is equivalent to saying that the particle that falls into the hole has negative energy).
Note that the Schwarzschild metric describes the static spacetime around a black hole that has already formed. It most definitely does not describe the non-static spacetime during the collapse. It is, in general, not wise to base any conclusions about the black hole collapse on any feature of the Schwarzschild metric such as the time dilation at the Schwarzschild horizon.
How does the particle get energy from the hole if nothing can escape the hole?? Never mind: for those interested, Kip Thorne describes several ways to picture this detail in BLACK HOLES AND TIME WARPS, beginning page 439.
"Nothing can escape from a black hole" is a broad-stroked statement that is perhaps too coarse for the subtleties of the subatomic world. Very roughly: It is a virtual particle. Virtual particles are produced in pairs from vacuum and separate upon creation. If they are very near the Schwarzchild boundary, one of the pair falls inward. With nothing to annihilate with, the orphaned virtual particle becomes real and exits the vicinity of the BH. In doing so, the net energy of the BH drops.