No, black holes can be partially contained in our causal present. According to GR that's true of e.g. the black hole that's believed to exist at the centre of our galaxy. The sun becoming a white dwarf is entirely in our causal future. Like I said, black holes, including the singularity itself, can overlap with our causal present. I don't know where you're getting this "infinite future" stuff from. Given all your talk of "objective reality" in the quantum physics threads, I'm surprised you apparently now can't make the distinction between something existing and our knowledge of it existing.
This is the second time you've done this, like you've caught me doing something. Is posting the same item on multiple forums disallowed in the forum rules? The reason I do this is because Physicsforums has stricter guidelines on what material is permissible for discussion, and generally their responses are on a higher level (no offense to the A-listers here). There is less "noise" there, which is probably why I've never seen you join in the discussions on that site. Yes, portions of the black hole exists in our future time line, but its existence prior to that is again presupposed in order for that time line to exist. As I raised at Physicsforums, the interior portions of the event horizon which are not in our future light cones are also not space-like separated from us today, nor are they light-like separated. This is why there we cannot state that black holes "exist" today...there is simply no reasonable definition which allows for the statement to be true.
I think you have misinterrpreted the information here, it was just an event for a bet that Stephen Hawking could never lose because it could never be proven via experiment. I would think he has a betting problem, but why not bet on something someone could never actually prove? I think the first work on this theory could have gone back as far as the 70's, at least the early 80's.
Utterly false, as the people on PhysicsForums are also explaining to you. Either a black hole is entirely in your causal future (i.e. it "hasn't formed yet", as in the case of a large star that's still millions of years from collapsing), or it's not and part of it, which can include part of the singularity itself, are in your causal present. In the latter case, as the people on PhysicsForums are also explaining to you, regions within the event horizon in your causal present are a finite spacelike distance from you, in the sense that you can define a spacelike curve between you and such a region of the black hole, integrate ds along that curve, and you will get a finite value.
Why wouldn't the particle pair be frozen in time to an outside observer? Any event near the event horizon would stop to the outside observer, so it wouldn't actually happen until infinity years later. So then how does this evaporation process ever happen if it is infinity plus .1 secound later to the outside observer? The outside observer could never see it happen. I think you may be right, there is no surface at the event horizon, but normally when something goes down onto something where it is forced to stop it is normally called a surface. I have read a bit about black holes, and they tend to think that neutrons are then converted to some other particle, but they don't know for sure exactly what that particle is. If it was a particle that could travel close to the speed of light, then it could probably slip right into the black hole, black holes are said to feed on surrounding stars and create jets. It doesn't suck in a nearby star and the nearby star just sits there frozen in time.
It would approach being "frozen" in time as the redshift got worse and worse. Eventually you wouldn't be able to see it any more with any practical means. Particle-antiparticle creation occurs at some distance above, not at, the event horizon. Thus it can escape. It does not stop; it just appears to stop. Traffic light cameras, for example, do not 'freeze" traffic even though it looks like the car isn't moving in the picture.
I'm happy with this so far. Which means we should recognise that it doesn't cross the event horizon, as per the original "frozen star" black hole interpretation. Which ought to lead us to think that it "piles up" at the event horizon, adding to the mass of the black hole. That's going to make the event horizon bigger. Keep doing this and the mass doesn't cross the event horizon, but the event horizon crosses it. The black hole grows like a hailstone. No problem. We claim that the black hole was created say a million years ago when some big star collapsed. Again no problem. Yes, it's presumption 4. IMHO it's the wrong conclusion. IMHO the right conclusion is that the original "frozen star" black hole interpretation is correct, and the more modern "central singularity" interpretation is incorrect.
The space-like definition I used disallows this. It may be true that space-like definitions must be reworded to be applied to GR, but, for example, the events between an observer on Earth and the formation of a black hole are not causally ambiguous. Also, I was referring to the proper length to the singularity rather than any point within the event horizon. If the singularity does not exist, the event horizon cannot either. It's simply not easy for me to work and battle multiple fronts from multiple respondents at the same time.
We disagree here Farsight. The event horizon would need to be able to grow without actually reaching that critical threshold of gravitational collapse. I believe it never actually occurs, but is asymptotically approached. There is no singularity; there is no event horizon; for all practical purposes, mass is unable to escape its pull but not theoretically so; light is infinitely red-shifted but not actually trapped. Of course it's the wrong conclusion! Please Register or Log in to view the hidden image! I worded the OP in the way that I did to avoid all of the prejudices that are associated with questioning black holes in science forums. I concur with the frozen star sentiment.
What definition? I hope you're not naively defining "spacelike" in terms of Schwarzschild coordinates. Hardly. The concept of light cones carries over from SR to GR virtually intact. Spacelike separation means that you can connect two events with a spacelike curve (which technically means that the tangent vector along the curve is spacelike everywhere along the curve). All these definitions are straightforward adaptations of the analogous concepts in SR: spacelike means ds[sup]2[/sup] > 0, lightlike means ds[sup]2[/sup] = 0, and timelike means ds[sup]2[/sup] < 0. You can quite literally read off the Schwarzschild metric for example that the r coordinate is actually timelike and the t coordinate is actually spacelike if r is less than the Schwarzschild radius. Yes they can be! For the umpteenth time, an event horizon can be forming in your causal present, which means it is neither in your future nor in your past lightcone. That can be spacelike separated from you too! Generally points on the singularity are also a finite spacetime distance or proper time away from you too. As far as I can see, the major contributors in your PhysicsForum thread are telling you exactly the same thing I am telling you. Unless you actually want to walk through the detailed mathematical study of black holes and check for yourself that everything we're saying is correct, I fail to see any basis for your continued disagreement with what you're being told.
RJ: If you concur with the frozen star, think about what you said on the other thread: "A frozen star would 'freeze' from the center, out". As it does, a region is growing. In this region light and everything else is frozen. Nothing moves. The coordinate speed of light is zero. So light is trapped there, and there are no more events. So the surface of this region is the event horizon! Whilst there is no central point-singularity, the event horizon is the original Schwarzschild singularity, which the "currently accepted model of black holes" treats as a coordinate artefact with no actual reality. I think it's worth me responding to a couple of posts from James and przyk on the other thread about this. You might care to sound out what I say elsewhere. It isn't pointless. Clocks "clock up" some kind of regular cyclical local motion. When the clock stops, that motion has stopped. It's "frozen". This isn't true. Read Kevin Brown's The Formation and Growth of Black Holes and note this: "Incidentally, I should probably qualify my dismissal of the "frozen star" interpretation, because there's a sense in which it's valid, or at least defensible. Remember that historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse." This section originlly referred to Misner/Thorne/Wheeler and Weinberg instead of Einstein and QFT, but Kevin Brown changed it. What's happened is that the MTW interpretation has "won", and now people don't know about the other interpretation. They think the currently accepted model of black holes is the only one predicted by GR. The section below should be enough to tell you that the MTW interpretation is wrong: "In both of these interpretations we find that an object goes to future infinity (of coordinate time) as it approaches an event horizon, and its rate of proper time as a function of coordinate time goes to zero. The difference is that the field interpretation is content to truncate its description at the event horizon, while the geometric interpretation carries on with its description right through the event horizon and down to r = 0 (where it too finally gives up). " In the MTW interpretation, the object goes to the end of time and back. See this page posted up by a guy called Jesse. The Schwarzschild chart on the left ought to go up forever, but it's been chopped off. Now see what I said to James above. The Kruskal chart on the right is effectively saying that if you put a stopped observer in front of a stopped clock, he sees it as still going, and measures a finite proper time as he falls in. He doesn't. He's stopped. He doesn't see anything, or measure anything, ever. You can't make a stopped clock tick by putting a stopped observer in front of it.
Just to be crystal clear about where we disagree, the 'freezing process' in this scenario is never complete. The coordinate speed of light is never quite zero, but asymptotically approaches it at the center of the collapsing mass where pressure is greatest.
This is what I'm using. If you can convince me that the proper distance between an Earth-bound observer and a singularity is finite, and that there is causal order ambiguity, then I will concede.
RJ: It has to be zero. If it wasn't, light would get out, and we'd see it. Think about it. Shine a light beam straight up. It doesn't slow down, it doesn't curve round, and it doesn't fall back like a cricketball. The only way it doesn't get out of a black hole is if it's stopped. Everything is stopped, including the collapse, including anything that could be classed as an event. I know I've mentioned it before, but do check out the gravastar article on wikipedia. It's described "as an alternative to the black hole theory" but it isn't all that different to the frozen-star interpretation. Think about our frozen region where there are no events and light doesn't move. Light doesn't move so you cannot measure space and time. Now look at this in the gravastar article: "This region is called a 'gravitational vacuum', because it is a void in the fabric of space and time". The frozen-star black hole interpretation similarly features a "hole in spacetime", so it's more of a black hole than the currently-accepted model with the central point singularity. See this Scientific American article. Note the mention of Robert B Laughlin, the Nobel Laureate who gave us the lowdown on Einstein's GR here.
I understand your viewpoint but my interpretation would be that the light never ceases to 'get out', it just does so in an asymptotically-redshifted manner such that we cannot detect it. The classic Schwarzschild analysis at the event horizon would apply here, except the "event horizon" in this case is r = 0.
I guess we'll have to agree to differ on that, RJ. You take a view akin to "you can never get to absolute zero" whilst I take a view akin to "water does freeze". In both cases we can't detect the light, so it's black. So as far as we can tell things go in but don't come out, so it's a hole. So it's a black hole, even if we're not quite sure what's going on under the covers. That'll do me.
I'm not sure what you're expecting here. You really want to study how the integration of spacetime distance along spacelike curves behaves in the vicinity of a black hole singularity? I'm not even clear on why you think I should have to convince you of anything, given that you haven't even explained how you managed to convince yourself that the distance was infinite in the first place. How did the burden of proof get shifted to me here?
That was inadvertent. What I should've said was "If I am convinced..." I'll look at things tonight, perhaps.
