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Value of g near a black hole (revisited) 
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#55
Mar712, 08:11 PM

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#56
Mar712, 08:25 PM

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#57
Mar712, 08:47 PM

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#58
Mar712, 09:24 PM

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#59
Mar812, 06:38 AM

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OK. The difference between the Senior members and myself is spacetime related, and furthermore is now well defined. It need not be restated here. I think we can all agree on at least that much :{)
The generally agreed position is that we, in the 'external' universe, cannot observe a clock, or anything else except perhaps another black hole, enter an event horizon in finite time, let alone 'rapidly'. I think this position has been locked in pretty firmly by PAllen, PeterDonis and others. This position necessarily implies that gravitational wave detectors can never detect such events. Given this I think it reasonable to consider two cosmological implications of the agreed view. 1) Several billions of dollars have been spent on gravitational wave antennas. At least some cosmologists (a large majority, perhaps) expect the antennas to detect black hole events within their limit of sensitivity. If the Senior forum members are right then those cosmologists are mistaken. The events will occur so slowly (in relation to the detectors) that the detectors will at best see them, in electomagnetic terminology, as smoothed DC. 2) The current cosmological paradigm assumes that black holes have grown in the past and continue to grow today. What alternatives exist? Did they all spring out of the primal event full blown? A deep dichotomy is felt. The insight (or madness perhaps) I am defending agrees with the cosmologists' expectations. I cannot see how the opposing view can accommodate them. My position has not changed since my opening post, but it has certainly become better defined from a cosmological perspective. Perhaps it would be more appropriate for a new thread to be started, possibly in a different forum, if members would like to continue in this new cosmological vein. Would a Senior member like to adjudicate (or arbitrate) on the proposition? In the meantime we can perhaps agree on a clearly shared opening position here. Thank you all. "Disability access is a Dalek Plot" 


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Mar812, 09:28 AM

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#61
Mar812, 09:47 AM

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Let's be clear about one thing. The statement that no one outside the horizon sees, or is causally influenced, by anything inside, does not imply that nothing exists inside. Let me describe Rindler horizon scenario. Two ships are accelerating together at 1 g for a long time. They have reached extremely near c. One of them runs out of fuel and stops accelerating. The other ship will see the out of fuel ship fall a little behind, but then become red shifted, clocks on it slow down and asymptotically stop; red shift grows to infinity.The empty ship becomes invisible. The empty ship is never seen to be farther than a short distance away from accelerating ship, as long as it can be seen at all. It is 'trapped' on the Rindler horizon. Of course, for the empty ship, nothing strange has happened. The other ship accelerates away from it, getting ever further away. The empty ship can receive signals from the accelerating one, but any signals it sends can never reach the accelerating ship (because the accelerating ship stays ahead of the light; no contradiction because it had a head start and keeps accelerating  no superluminal implication).
This scenario has much similarity to the black hole event horizon. 


#62
Mar812, 02:36 PM

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It is still true that light from events near the horizon takes longer to get out, even in the scenarios we have been discussing. But the fact that the infalling objects are of nonnegligible mass means that the horizon's radius changes during the process, which changes the rules, so to speak, that determine what information can escape. 


#63
Mar812, 05:42 PM

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I submit. I set a trap for the Seniors and it has been turned upon me.
In my last post I brought real black holes (as opposed to ideal ones which are likely to be rare) back into play by resorting to cosmological arguments. I can find no fault in PAllen's response. Once again I have to agree with everything said in reply, or at the least admit I cannot combat the arguments. I cannot feel comfortable with any description of gravity except 'that which locally distorts spacetime'. The only way I'll win this argument is if my view is supported by gravitational observations, which so far are nonexistent. Indeed it is the sublime silence of LIGO which has brought me into the gravitational fray over the last couple of years. But that's another thread. I have been interested in gravitation as distortion of spacetime for a long time, and it has become important to me to better understand as many of its implications as I can manage. Overnight (for me) I see PeterDonis has also posted. Thank you PD. I specifically had that point in mind when I included 'or anything else except perhaps another black hole' in my last post. I'm glad you pointed out that the exception applies to all nonnegligible masses. There is only one (nonmathematical) point from the entire thread that I have not truly grasped. I accept the concept that, as almost infinite energy is required to hover near the event horizon, gravity can be inferred to become infinite at the EH. My difficulty is that the singularity must be at a more distorted (i.e. deeper, in the image below) position in spacetime than the event horizon, and if this is so then spacetime at the EH cannot truly be said to be infinitely warped. I alluded to this when I spoke of the intrepid explorer subjectively exceeding the speed of light. My problem may simply be due to the impossibility of representing spacetime in three dimensions. (This image is believed to be unencumbered by copyright) My memory is that not many years ago such diagrams of black holes showed an infinitely deep gravity well at the singularity. However now a search reveals the vast majority of such images to resemble that shown here, with almost flat bottoms. Does this represent a paradigm shift or just lazy artists? 


#64
Mar812, 06:00 PM

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A quick addition to my last post. I don't dispute GR but neither do I believe it to be a complete theory yet. I expect a new class of experiments will shake a few ideas within the next decade. In particular I expect the constancy of G to be seriously questioned. If G is not constant either in space or time then all inferences from astronomical observations will need to be reconsidered.



#65
Mar812, 06:21 PM

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The curvature of spacetime is nonsingular at the event horizon. Being a bit more specific, we can say that the tidal forces on a body freely falling through the event horizon are finite. They're calculated in most textbooks, for instance you'll find the detailed calculations in MTW if you look. The tidal forces on a freefalling body are equal to and given by the appropriate components of the curvature tensor.
The tidal forces at the central singularity are not finite, nor are the components of the curvature tensor. Both go to infinity there. The tidal forces on an accelerating body are, confusingly, not quite the same as the curvature tensor. So the equivalence between the components of the curvature tensor and the measured tidal forces is strictly true only for a nonacclerating body. The details get technical, but are a result of Bell's spaceship paradox, where the front and tail of a rigid spaceship have to accelerate at different rates if the spaceship is to remain rigid. If the front and tail accelerated at exactly the same rate, the spaceship would have to stretch (this is like the string breaking between two spaceships that accelrate at the same proper accelration). The difference between the accelerometer readings at the head and tail of the spaceship could reasonably be interpreted as definiing a sort of tidal force. But there is no actual curvature of spacetime in this scenario, the spaceships are in perfectly flat spacetime. 


#66
Mar812, 06:29 PM

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Thank you pervect. I like Bell, and Wheeler too. But I can only read them in English translation (from the math).



#67
Mar812, 10:53 PM

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The key thing you appear to be struggling with is that you are trying to find one single "thing" that can be thought of as "gravity". There isn't. "Gravity" encompasses multiple phenomena, and they don't all "go together" the way one's intuition thinks they ought to. But our intuition is based on a very narrow set of conditions where speeds are small and all aspects of "gravity" are very weak, so they all kind of "look the same". GR has to handle a much wider range of cases, where "gravity" gets a lot stronger and the various phenomena associated with it start acting differently (like proper acceleration vs. curvature at the black hole's horizon). It's worth noting, however, that the "infinitely deep well" idea has problems too. The underlying issue is the temptation to think of the singularity as a "place"a location "in space". In reality, the singularity is a *spacelike surface*which means that the closest thing to it in our intuitions is an *instant of time*a "slice" of the universe (more precisely, of the portion of the universe that's behind the horizon) at a particular time. You can't represent "the universe at an instant of time", or "a portion of the universe at an instant of time" as a spatial point on a spatial diagram. It should really be a *separate* "spatial diagram" all its own. If you look at the Kruskal or Penrose diagrams on the page I linked to earlier, you will see that they make this obvious: the singularity is a hyperbola that goes from left to right in the Kruskal diagram, and it is a horizontal line in the Penrose diagram. (This is also why we say that the singularity is "in the future", and why it's impossible to avoid the singularity once you're inside the horizonbecause you can't avoid moving into the future.) 


#68
Mar912, 01:15 AM

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As an aside I attended a spontaneous lecture by Roger 23 years ago. Everybody was expecting him to talk of matters cosmological but he spoke for 100 minutes on quantum effects in the brain's microtubules! I remember it all the better because it was the first important public event I attended wearing paws rather than shoes. I missed the multiquote button re pervect's post above, but I smiled when I read of Bell's spaceship paradox. 


#69
Mar1212, 10:33 AM

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#70
Mar1212, 10:49 AM

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There is no disappearance or reappearance. I came up with an analogy on another thread. Imagine a chain of infalling observers. Imagine a pink flashbulb goes off beyond one end of this chain. Prior to the pink light reaching (say) the last observer in the chain, all prior infallers are seen as before the flash reached them. The moment the flash reaches the last observer is exactly the moment when this observer sees all prior observers flash pink. Thus, the moment the this observer crosses the horizon is the moment they see earlier infallers as of when they crossed the horizon. Factoring light delay, you deduce they all got hit with the flash before you, but you only see them flash pink the same time you do. Similarly, factoring in light delay, this trailing infaller deduces the earlier infallers crossed the horizon before they did. 


#71
Mar1212, 11:26 AM

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Okay I kind of see, but if the infaller were to get very close to the horizon (say one plank length away) and then move away, would that mean that they observed the previous infallers crossing the event horizon twice, once on the way towards it and them reemerging on the return journey?



#72
Mar1212, 11:35 AM

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 no earlier observer is seen to have flashed pink  the trailing observer can still, in principle, accelerate away from the light, and without ever quite exceeding c, stay ahead of it: see Rindler Horizon. At precisely the moment the flash reaches the trailing observer, all prior observer's flash pink, and no acceleration at all will catch light that has already passed. Sufficiently locally, all 'near horizon' phenomena are accurately described by a passing flash of light  because the event horizon is a light like surface. 


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