The problem is RJ doesn't know what he's talking about so any analysis he tries to do reflects that. Hawking doesn't say black holes don't exist as real natural phenomena just the classical version which doesn't take into account it's quantum nature and that spacetime is dynamic. He discovered that 40 years ago.
It's an interesting paper and real easy to read. You need to have some familiarity with the coordinate changes he introduces. Such as adS_CFT. But it's easy reading on that stuff also. In fact the adS-CFT is really interesting. Find a power point on it with pictures. I have one somewhere. If I find it I'll attach a link. You'll enjoy it since you like the science. How about the comments 'to be reminded what science Hawking has produced'. How does he do it?
You think your behaviour here is any better than this? What in the world are you going on about? First of all, that wasn't exactly my answer, and second, I'd already answered that question for you before, including [POST=3155980]in this very thread[/POST] several days ago. If that was all you wanted to know from me, why didn't our discussion in this thread end there and then? Answer: because you then wrote [POST=3155984]this post[/POST], which was not a question about whether black holes exist in reality. As a matter of intellectual honesty, if you discuss or try to argue against the logical or physical consistency of black holes, as you have done in this and previous threads, you don't get to change the subject when that line of discussion doesn't go the way you wanted it to. No I didn't. I rather pointed out that you weren't really addressing the nature of existence, and that I didn't see any real need for the discussion in the first place. Ill-defined. And with good reason. I wanted a source explaining where you got the idea that black holes couldn't overlap with an outside observer's causal present. Your source did not support that. I never asked for a definition of "now" in Kruskal coordinates. If you are alluding to treating constant Schwarzschild time -- a coordinate that is well known to be discontinuous on the event horizon and isn't even timelike inside the black hole -- as a definition of simultaneity, then why in the world should I accept that as a good definition? You did nothing to justify that, beyond throwing the phrase "physical meaning" around as if it were some magic pill that let you draw any conclusions you wanted about Schwarzschild coordinates. Coordinates seeming "natural" and having "physical meaning" does not preclude them from exhibiting purely coordinate singularities or other pathologies. Hardly. It's rather you who keeps evading the responses I give you. You wanted to see "the math" behind interior regions of the black hole being a finite spacelike separation from an outside observer. I gave it to you and you summarily ignored it, claiming it contradicted something you'd read elsewhere. The source you linked to turned out not to be saying what you attributed to it, and in fact only supported something I'd already told you before: that a black hole is never in an outside observer's causal past. You then responded with this: which is silly, because you've had an answer staring you in the face all along: the Kruskal construction is already an explicit theoretical example of how that could happen without leading to any physical or logical contradiction. (So the answer here would be: 1) have a black hole, and 2) stay the hell out of it.) You've done nothing but dismiss this model out of hand. You make retorts like this: without ever actually explaining what's wrong with the Kruskal black hole model. I am not going to agree that the Kruskal construction is "unphysical" just because RJBeery decrees it to be so.
If he thinks that solution to the EFE is unphysical he's pretty much saying the theoretical model GR is unphysical. This whole thread was about RJ being right but he didn't read the Professor Hawking paper so it didn't meet his expectations [the thread, BAM!. He seems to be confused about the relationship between theoretical and experimental physics as if it's irrelevant. He bases everything he believes about black holes on Schwarzschild remote coordinates. At least he seems to like you. Like I said in the other thread you can show the distance to r=2M is finite by integrating the distance component of the Schwarzschild metric. So this means we can show the distance from r_shell outside the coordinate singularity to r inside the coordinate singularity using the Schwarzschild coordinates. Not very instructive other than to confirm the distance to r=2M is finite.
Are black holes no more? To astronomers, the mess of fundamental physics at the event horizon has little to do with the immense gravitational fields produced by these mass sinks at the cores of galaxies, powering some of the most energetic processes in the universe. Astrophysical black holes still happily exist. What Hawking is saying is that, with quantum mechanics included, the notion of a black hole as governed purely by the equations of general relativity, the "classical black hole", does not exist, and the event horizon, the boundary between escape and no-escape, is more complex than we previously thought. But we've had inklings of this for more than 40 years since his original work on the issue. In reality, the headlines should not be "black holes don't exist" but "black holes are more complicated than we thought, but we are not going to really know how complicated until gravity and quantum mechanics try to get along". Read more at: http://phys.org/news/2014-01-grey-black-hole-stephen-hawking.html#jCp
paddyboy and brucep: My opinion existed prior to Hawking's paper, which forms no basis for it. I'm providing it as an "appeal to authority" for you, because you are apparently impervious to appeals to logic. You both insist that you know the truth which is currently unknowable; I have no time or need for discussions with tepid, retired intellects. OK...at the very least I think we've identified our point of disagreement. My stance is that Schwarzschild coordinates have a special physical meaning whereas Kruskal coordinates do not. Would you agree that if that were the case then the Kruskal treatment of black holes does not provide evidence of their existence? I'm definitely willing to concede, publicly and loudly, that black holes exist today and in reality if we can identify a coordinate system which 1) avoids the coordinate singularity at the EH and 2) exhibits geometric significance. From GRAVITATION (Misner, Thorne, Wheeler, pg 596), Physical interpretation and geometrical significance of the Schwarzschild coordinates: The book goes on to mention that these are not the ONLY coordinates with such properties, and identifies Isotropic Coordinates as another system which adheres to these criteria. Unfortunately, isotropic coordinates would continue to expose the same coordinate problem at the event horizon.
For anyone that's interested, there's an equation for doing what brucep explains at.... http://exploringblackholes.com/ "Exploring Black Holes" Edwin Taylor,John Wheeler. Pick chapter 'Curving' and on page 3-37 your find 'Zeno's Paradox'. It shows the distance and time to event horizon are finite. The equation (18) is in the box on page 3-15. In the infaller's own coordinate frame there is no coordinate singularity, so there's no hiccup at the event horizon. But, they do contain a real singularity at the black hole's center.
I have never expressed knowing the truth, as you put it. According to latest observational evidence BH's of the GR type exist. Like all scientific models and theories, that will stand until a better explanation comes along that invalidates the incumbent GR BH, or supports another different beast. Please read my previous post to this one.
Actually I understand the logic of GR and you don't. Pryzk understands the logic of GR and you don't. That's what you continue to show. Apparently you think GR doesn't do what it was derived to do? Your logic is pretty much irrelevant on this subject. This is complete nonsense and sums up your non argument. You said: " My stance is that Schwarzschild coordinates have a special physical meaning whereas Kruskal coordinates do not." Utter ignorant nonsense. Really? The Schwarzschild bookkeeper coordinates are remote frame dependent coordinates. Transform to the local proper frame and the physics is invariant. The distance is a proper distance and the tick rate is proper time. These are invariant because they represent direct local measurement predictions. Pryzk showed you the length measurement is invariant but you didn't get it. For the black hole case the coordinate singularity at r=2M is transformed away by local proper frame metrics. You haven't even figured out the difference between frame dependent and invariant. If you did you wouldn't make such a huge gaff in logic. To learn something you'll need to give up on 'having to be right'. I would bet you don't have a copy of Gravitation. I do and I've read it. You should have read my posts also. LOL.
It's interesting the derivation is presented right away. Allows you to concentrate on the physics of relativity rather than a frame dependent coordinate singularity. The theory is really a masterful work of art. All observations and measurements are valid with the local ones being invariant and the remote ones being frame dependent. The remote measurements made of the 'dying pulse trains' are frame dependent measurements predicted by GR. Dolan called this direct evidence for the existence of black holes. I agree with him and consider it empirical test confirming a prediction of GR. Sounds like you've been having fun.
It's a 'meaningless' argument RJ. "My stance is that Schwarzschild coordinates have a special physical meaning whereas Kruskal coordinates do not." I'd care about your 'stance' if you were looking to learn something. But you're not. So *plonk* for you until you start another bullshit thread about black holes.
Awesome reference, nimbus, thank you. However, I've been discussing distances passing through the EH, not stopping at it.
As with other posters that carry an agenda, you fail to consider all what I have said.....Agan, like all scientific models and theories, GR type BH's will stand until a better explanation comes along that invalidates the incumbent model, or supports another different beast. When you have a sufficiently supported model that invalidates GR type BH's, give us a call.
The irony here is that I'm not arguing against GR in any way, I'm arguing against the interpretation of GR that claims the EH exists today.
Obviously some distant objects, stars, BH's or whatever, may not be there "now" meaning of course, there 'now" on say Alpha Centauri We all know there is no Universal now. If Alpha Centauri disappears "now" as in its "now", that will equate to our "now"in about 4.3 years time. Otherwise, yes the EH of any BH we see now, exists now.
No, for a number of reasons: 1) Very simply, it's a non sequitur. "Physical meaning" is a vague catch-all that could mean anything, and it does not follow that a singularity in the coordinates represents anything physical just because you, me, Misner, Thorne, and Wheeler, or anyone else think the coordinates satisfy some value of "physical meaning". 2) Due to the coordinate singularity at the Schwarzschild radius, it's dubious at best to claim they have any meaning at all there (whether you think the singularity is physical or not). 3) General relativity, as part of its foundation, is based on the principle of general covariance (i.e. coordinate system independence). If you study general relativity in a course or from a textbook, or even from some of Einstein's original publications, literally the first thing you learn is how to cope with completely arbitrary coordinate systems in relativistic physics. So if you make any argument that requires treating some coordinate system as "special", I'd consider it contrary to the spirit of GR and view it with extreme suspicion. 4) Even ignoring point 3), arguing some principle of "physicality" based on Schwarzschild coordinates is hopelessly ad hoc and wouldn't generalise to the rest of GR. Most of the time, in GR, there is no coordinate system that has all the geometric niceties that Misner, Thorne, and Wheeler describe in the passage you quote from their book. So if you decide those geometric features are so important to you that you could never part with them, you really shoot yourself in the foot. You'd be unable to cope with any physical system in GR that didn't happen to be static and spherically symmetric. Misner, Thorne, and Wheeler list geometric features of Schwarzschild coordinates that are completely consistent with what I told you in the third part of [POST=3156938]post #66[/POST]. They also say of the coordinate singularity at the Schwarzschild radius: and so on, and soon quite happily go on to describe various other coordinate systems, including Kruskal-Szekeres. So however much "geometric meaning" Misner, Thorne, and Wheeler think the Schwarzschild coordinates might have, they plainly don't think it should extend to treating the Schwarzschild chart as special or the coordinate singularity as physical. I mean, really, what were you hoping to achieve by quoting Misner, Thorne, and Wheeler at me? "You must be wrong, przyk. Look, here's this book written by these famous authors who completely agree with everything you told me!" No they don't. Put \(r_{1} \,=\, r_{\mathrm{s}} / 4\) into the metric expression and see for yourself what happens. You'll find that the \(g_{rr}\) metric component is just 4 (by contrast with Schwarzschild coordinates, where it becomes infinite). The \(g_{tt}\) component is still zero, but that's hardly surprising since both charts use the same \(t\) coordinate. (Also, technically, isotropic coordinates don't all "adhere to the same criteria". A spherical shell in isotropic coordinates of radius \(r\) won't have a surface area of \(4 \pi r\) unless \(g(r) \,=\, 1\), which isn't the case for the isotropic version of the Schwarzschild metric you linked to except in the limit \(r_{1} \,\to\, \infty\).)
Ahh, parse what you said carefully: you are considering the "now" of Alpha Centauri to be our "now" in 4.3 years time, which means you're basing the definition of "now" as a function of distance and the speed of light (we'll ignore the fact that our "now" will be Alpha Centauri's "now" in ANOTHER 4.3 years in the future). Then you said that any "EH of any BH we see now, exists now". But how would you determine that? Visually? Mathematically? Either way you're going to run in to problems. We cannot see or otherwise detect a classic event horizon, and your method of using the speed of light and calculated distance is going to produce...infinity. By your casual definition of "now", event horizons do not exist today. If you'd care to give a rigorous, mathematical definition of "now" I'd be open to discuss it.
Stop there. If I can't get you to commit to anything, making no theoretical or qualified concessions whatsoever, then I'm just spinning my wheels.
