Lots of places, but here's one And I'm sorry but my initial suspicion of using Kruskal coordinates has only grown stronger over time - if we redefine space and time parameters to avoid math singularities we cannot then substitute those new parameters for our everyday usage. t and r have a physical meaning. Constant t in the Kruskal diagram is represented by straight lines passing through the origin...therefore you can see that connecting Region II with Region I is simply impossible. The entirety of the black hole is in the infinite future of any point outside of it, which means it does not and will never exist... Please Register or Log in to view the hidden image!
RJ, first I have to admit that I have not been following the discussion in any real detail. That said, above it sounds as if you are confusing past and future existence, as a "space like" occurrence with past and future as a "spacetime" occurrence. It often seems that discussions like this which involve GR and spacetime, rely heavily on how information is transferred by light, overlooking the fact that information is also exchanged or transferred by gravitational fields, independent of the transfer of information associated with the propagation of light. . . Though light cannot cross a black hole's event horizon, its gravitational field does! And the presence of that gravitational field itself represents an exchange of information, connecting the pasts and futures of objects and observers outside the event horizon with the origin of the gravitational filed . . . the black hole within the event horizon. Any claim that a black hole does not exist in our past and/or future, must explain its associated gravitational field, as a function of some other mechanism than our current understanding of gravity. Within the context of our current understanding and theory, gravity propagates at the speed of light . . . and yet gravity and light are not equally limited by the existence of event horizons. Note: While the curvature of spacetime described by GR describes the kinetics of gravitational fields, it does not explain the fundamental mechanics of the origin of gravity.
First of all, this is a plain contradiction. If you think gravity propagates bidirectionally through the event horizon whereas light cannot then gravity has indeed surpassed the "speed of light". Secondly, I've heard explanations in the past about the gravitational field emitted by black holes as being a relic of the mass which existed externally to the event horizon (possibly in the past). I'm not saying this explains anything, I'm passing on what I've heard. Lastly, you're taking an apparent paradox and demanding that *I* explain it. *I* don't need to explain anything regarding gravitational fields escaping the event horizon because my stance is that the event horizon does not exist. Perhaps you would care to explain it without the obvious contradiction you mentioned above?
Please Register or Log in to view the hidden image! We could use the terminology that reflects most closely what they are.....Gravitationally Completely Collapsed objects... Bit of a mouth full though...I'll think we'll stick to BHs
No, EH most certainly do exist, and no play on words will ever remove that fact. The gravity from the BH of course, is a fossil field that was already present before it ever became a BH...A concise and correct explanation.
This definition doesn't support you. It's equivalent to the more familiar definition which says that a black hole is the region of spacetime from which you cannot escape from the singularity. Think about it. If you have an event X in spacetime that is in the past light cone of "future infinity", this means that there's a timelike curve passing via event X that can get to "future infinity", successfully avoiding the singularity. Or, stated differently, X is not in the black hole, because an observer starting at X could escape the singularity. Conversely, if an event Y is not in the past light cone of "future infinity", then no timelike curve passing via event Y can reach "future infinity", so (barring really esoteric situations like closed timelike loops) the only alternative for any timelike curve passing via Y is to terminate on a singularity. An implication of this that I've already told you about is that a black hole can never overlap with an outside observer's causal past (in fact, it's probably the simplest way to define what it means to be outside a black hole). This has nothing, logically, to do with whether a black hole can overlap with an outside observer's causal present. The Kruskal chart quite clearly depicts both, for instance. Penrose diagrams depict this even more explicitly. We don't need to redefine anything at all. You're presuming that we first have to predict the black hole in Schwarzschild coordinates before we can transform to Kruskal coordinates. We don't. The black hole metric expressed in Kruskal coordinates describes a perfectly valid pseudo-Riemannian manifold that can be shown to be a vacuum solution to the Einstein field equation. It is, therefore, a perfectly valid prediction made by general relativity. It is no more than a matter for our history books that the black hole was first derived in Schwarzschild coordinates. There's no fundamental reason it couldn't have happened in the opposite order. So if there really were something fundamentally wrong with Kruskal coordinates and the Kruskal metric expression, you should really be able to point it out without having to make any reference to Schwarzschild coordinates. No. Schwarzschild coordinates are defined to have certain "nice" properties. Specifically, the black hole metric is static (time-independent) and spherically symmetric when expressed in Schwarzschild coordinates, asymptotically approaches the Minkoski metric in spherical coordinates in the limit \(r \,\to\, \infty\), and the locus of points at fixed Schwarzschild radius \(r\) at any given Schwarzschild time \(t\) constitutes a surface of area \(4 \pi r^{2}\). Kruskal coordinates are defined to have different "nice" properties. Specifically, their defining property is that radial null geodesics (light-like curves) always have a coordinate velocity of \(\pm 1\). The point is, both these coordinate systems are, first and foremost, defined mathematically. That's not to say they can't have any "physical significance", but that's not how they're defined, and if either does have "physical meaning" it's 1) a bonus and 2) only to the extent it can be justified from its mathematical definition and the corresponding metric expression. Both coordinate systems have their strengths and weaknesses that follow from their basic properties. For instance, the fact that the metric is static in Schwarzschild coordinates means that you can easily read off certain things (like relative Doppler shifts between observers at constant Schwarzschild radii) more or less directly from the Schwarzschild metric expression. The way the Kruskal chart is defined makes it particularly easy to see the causal structure of the entire black hole manifold. Neither of these coordinate systems is completely general, by the way, and it's only because the Schwarzschild black hole happens to be quite simple that we can even use these charts at all. If anything, if I'm to believe what I read on Wikipedia (specifically here), it's actually the Kruskal construction that is the more general of the two, since it seems that one can always find a conformally flat (i.e. "Kruskal-like") coordinate chart for at least two of the four spacetime dimensions. By contrast, most possible spacetime manifolds are not static or spherically symmetric, and therefore simply wouldn't admit a Schwarzschild-like parameterisation at all.
"So you can argue about whether singularities violate General Relativity or not until you’re blue in the face. It doesn’t have a damned thing to do with whether any light gets out of your ultra-dense, massive object. And that’s what we call a black hole, and it exists. Don’t believe it? Then tell me what’s going on at the galactic center." Are Black Holes Forbidden Mathematically? Did anyone post this video, yet? :shrug: [video=youtube;tEtt4A7WsDg]http://www.youtube.com/watch?v=tEtt4A7WsDg[/video]
This is my choice of coordinates for evaluating the proper path. Generally. Gullstrand–Painlevé coordinates http://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates Even the uninitiated should be able to conclude there is no coordinate singularity at r=2M. The uninitiated tend to think the only choice of coordinates are the Schwarzschild coordinates of the remote bookkeeper. At least it seems that way to me.
Hmm, how could something exist in our causal present but not in our causal past...after we've reached the future? The basis of our problem is that you're arguing pure math while I'm arguing physical reality. Claiming that Schwarzschild coordinates are "nice" in some ways, but otherwise arbitrary, is not true. I've already quoted what Misner et al had to say about the Schwarzschild time parameter and its special physical meaning from Gravitation (I guess I'll repost it when I get home). You're pointing at a Kruskal graph in an argument about PHYSICAL EXISTENCE. You've already conceded that the concept of what it means "to exist" lies outside of the realm of Physics...which is a statement I completely disagree with...but if that's how you feel why do you continue with all the nuanced obfuscation? Ignore everything else and just put it simply, przyk: in your opinion, do event horizons exist today?
Great link, and what I have been saying all along. And it applies to all mainstream theories......Those that purport they are wrong, must have something that either falsifies them, and/or explains to a greater depth, the subject in question.
Please Register or Log in to view the hidden image! I did make a reference to this somewhere. Hawking is well known for his sense of humour and taking the Mickey out of people.
I've already answered this; an ultra-dense massive object from which light takes asymptotically longer to escape as one gets closer to its center. It would appear black, or very close to it.
Why, precisely, can't you take the black hole solution, in Kruskal coordinates, as a theoretical example of exactly how that might be possible? I even previously gave you an example of how a similar situation arises for a constantly accelerating observer in special relativity. The only objection I remember you were able to come up with -- that indefinite acceleration requires unbounded energy -- doesn't carry over to the black hole situation. I am arguing in terms of general relativity and in terms of its foundation in pseudo-Riemannian geometry. If you don't discuss in those terms, you are discussing something that is not general relativity, in which case, as far as I'm concerned, you are free to believe whatever you want to believe about whatever hypothetical theory you are thinking of. And I thought I was already quite clear on the fact that general relativity is not necessarily the same thing as reality, and is in fact very likely not an exact model of reality. I didn't deny that Schwarzschild coordinates could have (some) physical meaning. What I said is that whatever physical meaning they do have needs to be carefully justified from how they're defined. You can't just blindly believe anything you want to believe about them. Most importantly -- and I really can't stress this enough -- there is nothing in how Schwarzschild coordinates are defined that actively safeguards against a coordinate singularity arising. You're pointing at misbehaving coordinates and telling me that must represent something real based on, at best, hopelessly handwavy and ad-hoc arguments that have little to do with the foundations of general relativity. Physics starts with the premise that things exist and that we should study and learn about them. Your past threads didn't remotely touch on the nature of existence. You were rather concerned with how the present tense of the verb "to exist" should be used in the context of relativistic physics. That is a linguistic matter, not a physical or even philosophical one, and the lesson I'd learn from it is that our centuries-old grammatical traditions are very poorly suited to discussing and understanding foundational issues in 20th and 21st century physics. There's two ways you can react to this: Complain. Learn a more suitable language, like Riemannian geometry. Why do you insist on simplistic, definitive answers to questions that aren't simple? "Today" is frame-dependent according to special relativity and it's even less well defined, if it's possible to meaningfully define at all, in general relativity. Singularities and event horizons very likely exist in my causal present, according to GR, based on the observational evidence we have. But, I stress, I am under no obligation to believe that GR is an exact model of reality. I honestly don't know if black holes, or some analogue of them, exist in reality. Not only do we lack a theory of gravitation that is expected to apply at the quantum scale that I could base my expectations on, but I'm not remotely an expert even in the educated guessing that some gravitation specialists are engaging in today. The biggest mystery for me reading through your threads is why you feel so strongly you need to have any opinion on black holes at all.
well, i've previously posted the video in your link showing stars in orbit about the BH at the center of our galaxy. http://www.zmescience.com/space/closest-star-black-hole-orbit-milky-way-20313/ http://io9.com/the-video-that-revealed-the-black-hole-at-the-center-of-1114918644 http://www.astro.ucla.edu/~ghezgroup/gc/pictures/orbitsMovie.shtml
Unfortunately much of this becomes 'who's going to admit they're wrong' about anything much less science. Nobody. Apparently. Some folks don't get to admit they're wrong very often and look forward to it as evidence of their humanity. As far as black holes are concerned they exist as real natural phenomena. The dying pulse train is evidence for that. That's why Joe Dolan was looking for evidence of the GR prediction in the Hubble archives. That prediction is derived from Schwarzschild coordinates. A frame dependent prediction. Evidence that frame dependent observations are as valid as invariant measurements. What clearly doesn't exist, as real natural phenomena, is a black hole that is only described by GR. Big surprise that it's a quantum object like everything else in the universe. In essence the classical black hole is an approximation derived from the classical theory. Is it surprising that the coordinate singularity doesn't remain at fixed coordinates in a dynamic spacetime? No. Hawking destroys the 'Firewall hypothesis' in his paper. Should be interesting to follow future discussion on the subject of 'Firewall'. His analysis is what's interesting not what some amateurs think it means.
Because I am both frustrated and fascinated to witness the lengths to which people will hold on to their beliefs, even when they are logically incapable of defending them. Example: Paddoboy, you might as well replace "EH" with "Angels in Heaven" with a statement like this because it does not belong in a scientific discussion. Et tu, przyk; you disappoint me sometimes. Even when you are tacitly conceding a point, it feels like you are trying more to ensure that the point is minimized than actually discuss Physics. Rather than just saying "no, I don't believe black holes exist today" you dive in to comments about how existence is meaningless in Physics and today is meaningless in GR. It's not even that you're wrong, per se, it's that you seem to do everything you can to ensure that we have no common ground. You wanted citations for "infinite future", done. You wanted a definition of "now" in Kruskal coordinates, done. You summarily ignored both and moved on to basically just asking me to accept that black holes exist today because...Kruskal. Anyway, whatever. I'm not here to change opinions, only to gather information. Even though much of this forum is noise I do get some good stuff from time to time and I appreciate everyone's contributions...
Thanks for linking the discussion. Hawking shot the firewall down so this should get interesting. The firewall hypothesis never sounded right to me. It breaks the cardinal rule that the quantum gravity theory will recover GR in it's domain of applicability. It doesn't. Professor Polchinski seemed a bit conflicted about this. Dude is one of the big brains. Clash of the big brains. Hawking and Polchinski.
Blacks holes exist regardless what you want to believe. You should have started a thread on the Hawking paper rather than trying to use it to prove you were right in previous threads on the subject. You might want to read it.
That's your biased opinion. One paper does not a summer make, and the way you see the need to jump on it, shows that bias brilliantly. Again GR type BH's most likely do exist. And until someone can explain another way the observations we do see, they will always exist. I'm sure Stephen would overwhelmingly agree, despite his paper.
These coordinate metric equations are solutions to the Einstein Field Equations. So they're wrong? GR's bullshit?
