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md65536

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md65536 last won the day on May 25 2023

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  1. Or use wheels that are the same size and curve the road intrinsically... like with a trampoline. How is your analogy "correct"? What do the wheels represent and are you saying that spacetime (the road) is not really curved??? This also shows that gravity is not needed to show curvature in the trampoline analogy. Pin a rubber sheet flat against a wall in zero-g. Stick a large ball representing a gravitational mass under the sheet, stretching it (or even a long pipe sticking out from the wall, to imagine it more extremely). Roll an axle with 2 wheels of the same size along it, and the path will curve, analogous to null geodesics.
  2. Then the radiation field of an accelerating charged particle drops off as 1/r because it propagates perpendicular to the acceleration of the charge, the field lines distributed over a circle for a given r rather than a sphere? An oscillating charge radiates EMR with a frequency equal to that of the oscillation. Apparently, Maxwell's equations imply that even a charge with a constant acceleration must also radiate. However, the frequency and energy would be zero, or at least approach zero as time approaches +/- infinity. So one could say that a charge at rest on the surface of Earth does not radiate energy, or that it radiates light with infinite wavelength, which is not physically detectable nor has an absolute meaning, but is consistent with all physical laws. I hope this is right instead of me just getting more confused.
  3. I don't know! Is it all/only electromagnetic radiation, ie. photons? I see references to "radiation field", but it's described separately from the electromagnetic field? I assume that if electromagnetic radiation is detected, that means a photon is emitted at one event and absorbed at another event. That seems at odds with the quote from the paper, "the detection of radiation has no absolute meaning", so I'd already concluded my assumption of EMR was wrong. Then I (mis?)interpreted the quote as a description of what the radiation is, as something that remains when things like EMR are separated out. Doesn't EMR drop off as 1/R2? It's all very confusing...
  4. I read https://arxiv.org/abs/physics/0506049 [1] from swansont's earlier link, and it clears up some of my misconceptions. The basic conclusion, in the case of a comoving observer and a uniformly accelerated charge, is that there is only a certain region of spacetime that "would allow us to detect unambiguously the radiation emitted by the charge," and that region is outside the light cone of any event on the particle's world line, meaning that no radiation is detectable at all. Within the light cones, "the detection of radiation has no absolute meaning because the detection depends both on the radiation field and the state of motion of the observer." So I guess if you wanted to argue that any radiation could be detectable, you'd have to be really creative with definitions in order support that conclusion. Also it is not electromagnetic radiation as I'd assumed. "The radiation content can be extracted by separating the components that drop off as 1/R from the usual Coulomb 1/R2 fields." 1. The radiation of a uniformly accelerated charge is beyond the horizon: a simple derivation Camila de Almeida, Alberto Saa
  5. Oh, right. I see that was already resolved earlier. The frame where no light (of any wavelength) is radiated is an accelerating frame.
  6. What does this mean? Wouldn't it radiate as light? If so, what frame wouldn't it radiate in? Isn't the problem that if there was radiation, the expected energy would be undetectably low?
  7. Yes, what I described, at the limit where the BH can be removed leaving just the photon sphere, fits the definition of a geon. I can't imagine that such a spherically symmetric shape wouldn't work, and that a geon needs a different shape.* It would be unstable because if any photon deviated slightly outward, its orbit would be wider and it would escape, leaving less energy, reducing the photon sphere radius and letting other photons escape. I imagine a photon deviating inward, without a central BH, would cross the photon sphere again and escape, but I'm not sure (maybe it could collapse the geon?). * Actually, I see Wheeler's 1955 paper "Geons" describes this and interesting complications I hadn't thought of. PDF: https://blackholes.tecnico.ulisboa.pt/gritting/pdf/gravity_and_general_relativity/Wheeler_Geons.pdf To make it stable, it would have to be a quantum geon. Those are theoretical only and seem to require quantum gravity. I guess the basic idea is that if energy can only leak in specific amounts, one could be coherent enough to prevent that. There are papers on them but I haven't yet found anything I can make sense of.
  8. I'm interested in any situation or metric, or any simplification (or complication) involving a system of trapped light and a minimum of anything else. (Now that I say that, I have a vague memory of well known physicists speculating on astronomical objects made of light itself, gravitationally bound to itself but not collapsed, but I can't remember what they're called and I think that might be harder to reason about.) It does seem like if you think of the system of a black hole and a photon at 1.5 rs with at least as much energy as the black hole, and consider it inside a sphere of size 2 rs, it should collapse, but that assumes all the energy is contained within that radius, but it is not spherically symmetric, and it should have angular momentum (unless you contrived it not to by giving the BH itself the right angular momentum, but that just further complicates things), and like you say Markus, the Schwarzschild metric can’t be used. It also seems like all these complications are just more "stress" than a Schwarzschild case, and more certain to collapse. But are there ways to remove stress from the system so you could increase energy without collapse. eg. a cosmological constant. What might happen if the original photon was moved farther away to avoid collapse, such as at the photon sphere of the new black hole you describe? Or to make it symmetric, many uniformly distributed photons in a photon sphere. It seems like in general, for a real black hole photon sphere of a given size, if you add more energy to the photon sphere, you could get away with a smaller black hole, to the point that you don't need the black hole at all (which sounds reasonable now that I remember the idea of objects made of gravitationally bound light).
  9. I shouldn't have used the word "stable", what I meant was just "circular orbit" for some time (several orbits or so) because apparently circular already implies it's on the photon sphere. A bit of a digression on this: I see in https://en.wikipedia.org/wiki/Photon_sphere , "all circular orbits have the same radius". At the event horizon, light aimed directly outward will have a constant r, and at the photon sphere, light aimed tangentially will have a constant r. Is that correct? Then, everywhere in between, there is some direction that will let light have a constant r. These photons would circle the black hole, but they're not called circular orbits?
  10. I figure they would because their orbits should have an effect on the electromagnetic field detectable at a distance?
  11. Is it possible trap light in a stable circular orbit around a tiny Schwarzschild black hole such that the energy of the light is greater than that of the black hole?
  12. You should still be able to model a universe with an absence of light without removing the rules for it, such as a universe made up only of dark matter, or maybe including uncharged black holes. You'd have to make assumptions, but in accepted models, energy/mass equivalence holds for dark matter on its own.
  13. I'm struggling to figure out your meaning relating to previous posts. This represents the timing of events along the length of say a train, in a particular inertial reference frame? But the rate is slower than c, which would mean those events cannot be simultaneous in any frame. Are you using the composition of velocity calculation to figure out the velocities or at least check that they make sense? It seems like you should be doing that here.
  14. I looked elsewhere and it looks like "coordinate velocity" and coordinate speed are terms that are used and understood. Yes there's no flaw in relativity here. Alice and Bob, using their different respective local coordinates, disagree on the coordinate speed of light in empty space, just as GR predicts they should.
  15. For example, in Schwarzschild coordinates, the rate at which light propagates at the event horizon is zero, but still the local speed of light at the horizon is c. Obviously both things can't be referred to as "the speed of light" and be used interchangeably. I used "rate" instead of "speed" because I don't think the latter is the right word to use here. What's the correct term for what you're describing (or for what Bjarne-7 is having a problem with?). I wouldn't use "speed of light" when talking about curved spaces unless whatever d/t that's referred to is the same as the local speed of light over d. Anything else I think needs to be described more specifically than just "speed of light."
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