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This excellent answer to Could dark matter exist in the Universe in the form of sufficiently dense objects? includes the following image and description:

Black Hole light paths Light from the background galaxy circles a black hole an increasing number of times, the closer it passes the hole, and we therefore see the same galaxy in several directions (credit: Peter Laursen).

and illustrates three strong gravitational lensing light paths from a source to an observer. In this not-drawn-to-scale illustration, each path is shown reaching the observer from a close, similar direction, but they represent very different trajectories; one is a simple bend, the second makes a complete ~360° loop around the black hole, and the third a double ~720° loop-de-loop.

Conservation of etendue is how optics folks view conservation of phase space (Liouville's theorem).

Familliar examples might be understood from the impossibility of concentrating blue sky with a magnifying glass, or that a wall does not appear darker when you walk away from it despite $1/r^2$.

Question: How well conserved is etendue in extreme gravitational lensing scenarios?

In "normal lensing scenarios" like the use of telescopes, they can never increase the apparent luminance of an extended object no matter how large the aperture. But in some gravitational lensing scenarios and real-world searches, dramatic brightening of objects occurs.

Are those, or the scenario in the illustration examples of breakdown in conservation of etendue?

uhoh
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  • a terrestrial loop-de-loop – uhoh Jul 31 '21 at 01:39
  • A good question, but perhaps physics.SE would be better? – pela Jul 31 '21 at 09:17
  • Your questions are thought provocing. So is this one. Im not sure if this is the place to ask but luckily you did. Im not sure if a photon can make a trip around a black hole as is pictured. A mass cant make such a trip around a planet or star. It would be a smooth differentiable closed curve. On the other hand BH's are not planets or stars and photons dont have mass. Ill look deeper in this question.:) – Deschele Schilder Jul 31 '21 at 11:01
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    Its not phasespace that is conserved but distributions in phasespace. Around every point in phasespace the density of points closeby is constant. Which doesnt mean the points cant smear out. – Deschele Schilder Jul 31 '21 at 11:07
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    @pela my questions are a lot more successful here than they are there. Because the question rate is so high there, Physics SE folks will often scan for the low-hanging fruit and avoid questions that don't have textbook answers or answers that can be plucked from recent papers. I'm also not sure that "How well conserved is..." will fly there, they are pretty quick with the "unclear what you're asking" close votes; if you are not pretty sure just what kind of answer you'll expect, it only takes three question closers to shut everything down assuming the insta-close experiment is still running. – uhoh Jul 31 '21 at 14:16
  • @pela so let's see how things go here for a while first. – uhoh Jul 31 '21 at 14:16
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    @uhoh Fair enough, I also rarely go there anymore, actually. – pela Jul 31 '21 at 16:54
  • @pela I think it would work better if it were subdivided. Smaller SE communities are often more cordial and/or collegial exactly because they are a little bit more like waking down the hall, grabbing a piece of chalk and posing a question than the larger ones – uhoh Jul 31 '21 at 21:15
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    @uhoh Not a bad idea. Another way would be to subdivide into fields, simply to make each one smaller. If we can have astrophysics/astronomy as a separate site, I guess we could also have mechanics, solid state, fluid dynamics, etc. – pela Jul 31 '21 at 21:21
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    I would like to add to @DescheleSchilder's excellent point that, in terms of wave optics, this distribution-conservation (etendue) only holds under the paraxial condition, in that paraxial-Helmholtz equation = Fresnel diffraction = constant in etendue = the phase-space representation, and this "amount" of etendue depends on the wavelength. I cannot comment more on the question itself due to my lack of expertise in gravitational lensing. – WDC Aug 01 '21 at 08:36
  • @WDC Oh that's a very helpful answer right there! Please consider posting it as such. One can replace the black hole with anything that strongly deflects light; a ball lens, a bag of marbles, etc. If there's any real-world example of etendue conservation breakdown anywhere I think that's sufficient. – uhoh Aug 01 '21 at 08:41
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    Great comment you made about the low-hanging fruit!. I think this is indeed the better site. – Deschele Schilder Aug 01 '21 at 09:22
  • @DescheleSchilder I can understand suggesting to post there since there's plenty of great optics and GR well-answered questions. But there are also plenty of great questions that go unanswered, or that get answers which are unhelpful. Here in Astronomy SE there seems to be a better sense of community and care for questions, both in improving them and in getting them answered. – uhoh Aug 01 '21 at 09:23
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    Not answering because I don't have enough on hand to back this up, but in the case of gravitational lensing, it's not that the source gets brighter because of a failure to conserve etendue, but rather more light is reaching your eyes due to the lensing than would otherwise. What you have to consider being conserved here is the total amount of light the source is emitting, not the total amount of light you observe. – zephyr Oct 08 '21 at 17:27

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