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Relative energy of a black hole. 
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#19
Feb2312, 07:26 AM

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#20
Feb2312, 08:31 AM

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Don't want to appear sulky about that, but honestly, if you actually believe the issues in #10 have been well answered, how about your own detailed summary afresh? I have never been able to figure out effective searching using PF. As someone willing to endlessly discuss oft repeated SR/GR topics, this shouldn't be a hard ask surely. I could and if pressed am willing to reference back to that earlier thread, but prefer we leave that baggage behind. Oh, and I should thank you for at least stepping up and actually breaking the silence. Now if it seems like thread hijacking just say so and I will launch the issue(s) under my own banner. 


#21
Feb2312, 08:55 AM

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site:www.physicsforums.com Regarding the rest, the fact that you are aware of the previous responses on this topic and consider them all unsatisfactory seems to indicate that further discussion will probably lead to the same result. As you point out, when available we are often willing to devote many fruitless pages to topics that we notice which we consider interesting at the time. It appears that nobody with any current interest and availability has noticed your #10. For me, the lack of interest is simple exhaustion on the topic, which is a temporary condition but present now. 


#22
Feb2312, 09:15 AM

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#23
Feb2312, 09:43 AM

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#24
Feb2312, 05:44 PM

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Hi Qreeus, I just came across this thread and read your post #10. It's been some time, but I know I've given the simple classical answer to this in at least one thread on PF. (Unfortunately it doesn't appear that that thread was one of the ones you've participated in). The simple classical answer is that the "field of the black hole" doesn't actually come from inside the hole; it comes from the past, from the object that originally collapsed to form the hole. That is actually what the Usenet Physics FAQ page you linked to means when it says that the hole's field is a "fossil field"; it's a stationary remnant left by the collapsing object.
IMO, the FAQ page's mention of virtual particles is a little misleading since it invites the interpretation that the BH field actually does come from inside the hole, but somehow virtual gravitons can escape because they can move faster than light. Even on a quantum view of gravity I don't think that's correct; I think the explanation I gave above still applies. (Which is not to say that there is not a sense in which virtual particles can travel faster than light; there is. I just don't think that sort of thing is needed to resolve the question of "how gravity gets out of the black hole"it doesn't have to get out because that's not where it's actually coming from to begin with.) 


#25
Feb2312, 10:39 PM

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Now it has been stated that one must 'read between the lines'; meaning in effect that the nonlinear character of gravity in GR is evidence 'gravity gravitates' there in some de facto sense. I'm not convinced of that reasoning. The mere fact that matter induces curvature demands nonlinearity  rulers and clocks necessarily vary with distance from source, but this of itself does not imply any further contribution to curvature from that curvature. I don't particularly like citing authorities, but to back that point up, here's a quote from a Sascha Vongehr who at least styles himself as knowledgeable in GR: "All you need to be clear about is that pressure is part of the pressure energy tensor, i.e. part of the physical source of what happens in general relativity, one side of the Einstein equation. Gravity is on the other side, and it is not a source. It does not somehow walk around to the other side and become pressure, it is plain curvature in spacetime. It is nonlinear and so on, so it looks to us like a force that selfinteracts (= being its own source)." (last paragraph at: http://www.science20.com/comments/50..._gravitational) Don't know whether that qualifies him as 'crackpot' but clearly he has studied the subject and came to that conclusion. Is there actually an overwhelming consensus position on 'gravity does/does not gravitate'? Regardless of the source of BH gravity itself, the issue of charged BH presents a headache for GR imo. Again as stated in #10, one either posit that a static electric (or magnetic) field can act as it's own source (and where would that leave Maxwell's linear eqn's and the definitions of EM fields wrt to potentials, which in turn are defined wrt source charge/current), or one posits something truly magical imo. Namely that infalling charged matter, already at or interior to the EH, can continue to act as a continual source of vp (virtual photon) exchange with the exterior regions  despite all temporal processes ceasing wrt the exterior. If I'm missing something obvious here, please enlighen. Bet you wished already to have not bitten this one! 


#26
Feb2412, 12:01 AM

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#27
Feb2412, 03:49 AM

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"The Weyl tensor differs from the Riemann curvature tensor in that it does not convey information on how the volume of the body changes, but rather only how the shape of the body is distorted by the tidal force. The Ricci curvature, or trace component of the Riemann tensor contains precisely the information about how volumes change in the presence of tidal forces, so the Weyl tensor is the traceless component of the Riemann tensor." That part is fine, and intuitively it's obvious that in a nonzero matter density region curvature will be different than in vacuum regions. Which has similarity to the case in EM where divergence is nonzero only where charge density is nonzero. But then: "In general relativity, the Weyl curvature is the only part of the curvature that exists in free space — a solution of the vacuum Einstein equation — and it governs the propagation of gravitational radiation through regions of space devoid of matter. More generally, the Weyl curvature is the only component of curvature for Ricciflat manifolds and always governs the characteristics of the field equations of an Einstein manifold." What I get from that is that the exterior static field is a solution of the vacuum Einstein eq'n. So then, you are saying in effect that the latter is quite disconnected from the SET? But what then is the mass of a gravitating body other than an integration over the relevant SET for the matter region? And surely you cannot deny that for any static gravitating body, it's mass M determines the field. Going back to the analogy with EM, while it's true divergence is zero exterior to a charged region, it's equally true the divergencefree field in that exterior region derives from the charge and nothing else! Yet it seems something totally different applies in GR. I need a clear statement: if the exterior, Weyl curvature field has no source in the SET (i.e., mass = integrated stressenergymomnetum), what is it's source? So far this is how I see it. Your position is that both gravitational and electric fields exterior to a BH can be indefinitely sustained, based on past connection to mass/charge. But is that more than just bare postulate, albeit a standard one in GR? Without a position such as 'gravity gravitates', or an attempt to explain connection between exterior and interior 'original' source matter/charge, seems to me such fields are held up by mathematical fiat lacking any real underlying principle. My layman's prejudice perhaps. 


#28
Feb2412, 08:39 AM

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The BH case is the same thing, except that, because the gravitating body has collapsed behind an EH, the past light cone of any event in the exterior region only includes the collapsing body *before* it fell behind the EH. That collapsing matter in the past, before it fell beneath the EH, is what corresponds to the Sun eight minutes ago for us on Earth. The collapsed matter inside the EH is irrelevant to the field observed in the exterior, just as the Sun's state "now" is irrelevant to the field we experience on Earth "now". Of course, in the case of the Sun, we will soon know what the Sun's state is "now", by observing the field eight minutes from now, whereas an observer in the exterior region will *never* know the state of the collapsing matter inside the EH, because he will never get an "update" from that region; but again, that is simply because the matter in the BH case has collapsed behind an EH, whereas the Sun has not. http://en.wikipedia.org/wiki/Mass_in_general_relativity (See the section on the Newtonian limit for nearly flat spacetimes.) For a BH spacetime, you can't assume that the spacetime is "nearly flat", so the Newtonian limit doesn't apply. But the more general methods discussed in the Wiki article (ADM mass, Komar mass, etc.) still work, because they only require the spacetime to be stationary and/or asymptotically flat, and a BH spacetime meets both of those requirements. But you'll notice that none of those methods require a nonzero SET! Basically, in a stationary and/or asymptotically flat spacetime, you can come up with a workable definition of "energy stored in the gravitational field", which cannot be done in a generic spacetime without those special properties. It then turns out that a BH's mass is *entirely* composed of "energy stored in the gravitational field". 


#29
Feb2412, 11:28 AM

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#30
Feb2412, 01:35 PM

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But even the above English version has problems (one is that I have implicitly assumed a notion of time in several places in the above, without saying what notion of time it is). Ultimately, if you want to be sure you are understanding things correctly, you *have* to look at the math. The best summation of the math that I can give in English is this: (1) The observed "field" at any given event is entirely determined, ultimately, by what "sources" are in the past light cone of that event; (2) A "source", as used in #1 above, is a region with a nonzero stressenergy tensor. If you find yourself asking questions, in English, that don't seem to be addressed by the above, then that's probably a sign that English is leading you astray. "Does gravity gravitate?" is, IMO, one such question; see further comments below. The plain answer to how this picture is expanded to account for quantum phenomena is that nobody knows for sure. We don't have a theory of quantum gravity. We do know how to do QFT in a curved spacetime, where the spacetime itself is treated classically (but possibly with quantum "back reaction" terms added to the stressenergy tensor); in that picture, causality still holds and the explanation I gave above of fields being determined by sources in the past light cone, is still essentially correct (both for gravity itself and for the EM field of a charged BH). The only thing that QFT in curved spacetime really adds to the classical picture at this level is Hawking radiation: black holes can slowly evaporate. But that doesn't change anything I said above. My personal opinion is that, even when we do have a good theory of quantum gravity, its classical limit will still be GR, so it will still look like the picture I described above. The only way a complete quantum gravity theory could change that picture, IMO, would be if we somehow discovered that BH's can't exist at all: that there is some large quantum correction to the classical behavior that prevents event horizons from ever forming in the first place. But that would take away the problem we are discussing here altogether. 


#31
Feb2512, 04:53 AM

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Peter; on the matter of BH E field source. You at least have a consistent position, in the sense of not changing position from one entry to another. I fundamentally disagree with your viewpoint so there can be no headway and best we drop that part here. I have something in mind for a new thread attacking it all differently, but later. Now on the issue of whether gravity is a source of further gravity, I cannot see a consistent position, even though in any given response you come across as presenting one, when I check against other statements I'm getting a mixed picture. On the one hand, there is this from #28:
1: But then this from #30: If I didn't know better, could swear you're out to drive me insane. Saw both movie versions of Nineteen Eighty Four a while ago. Recommended viewing. In the end, O'brien the interrogator breaks poor old Winston Smith, who, with tears of joy, truly believes that when four fingers are held up to his face, there are really five. I have no tears of joy, just a frown. A little melodramatic, but what I'm saying is, please explain what seems to me are irreconcilable statements. 


#32
Feb2512, 06:26 AM

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#33
Feb2512, 06:37 AM

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Prepared to make good on that one  like 'soon'? 


#34
Feb2512, 06:56 AM

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#35
Feb2512, 07:05 AM

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#36
Feb2512, 07:20 AM

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