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I have recently discovered this question on Physics SE about photons doing loops around black holes (BH). There is a nice picture showing how a loop around a BH makes the observer "see" duplicates of the same far object.

There are good answers too and comments leading to related mirroring / seeing yourself showing a deep field JWT photo full of galaxies with a fascinating question

Is it possible somehow that one of the galaxies in such pictures is actually the image of the Milky Way?

that I intend to expand here.

The answer(s) from @PM-2Ring prove that

In theory, it's possible, but in practice it's extremely unlikely. The deflection angle is small unless the light ray passes very close to the centre of mass of a compact lensing body

What PM 2Ring seems to prove in his diagrams is that angles of up to 90$^o$ are not that impossible, even if mirror is harder, duplication seem likely (observing both the direct view and the deflected view) - especially considering the huge number of galaxies that we seem to be observing. A mirror means two deflections of 90$^o$, that would be enough to see yourself.

And if I go back to the previous photon loops question and the brilliant answers and simulations (also PM 2Ring), I come to a similar conclusion - if full-loop is possible, half-loop is like a mirror - so not that "extremely unlikely"?

Also, "deflection angle is small" is not that convincing, although I'm not that sure about the distortion. All the arguments here consider a theoretical single ray of light deflected, what happens with a "group" of rays coming from a distant galaxy? Would that still look like a "galaxy"?

I mean, am I right thinking that if the "lens" is rather closer to us (observer) than to the source, then the group distortion is smaller / negligible, so duplication is possible / likely especially with deep-space objects?

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  • $\begingroup$ Also noticed the brilliant Comment to the second (mirroring) question from @paul garrett: "possibly several different ages and versions [...] Also, not just about gravitational lensing, but about weird geometry of the large-scale universe?" a fascinating / separate (?) question on itself. $\endgroup$ Commented Mar 12 at 16:20
  • $\begingroup$ Also related more recent, with good answers that actually led me to find the older questions. $\endgroup$ Commented Mar 12 at 16:28
  • $\begingroup$ This question is similar to: Are there any mirrors in space?. If you believe it’s different, please edit the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem. $\endgroup$ Commented Mar 12 at 17:39
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    $\begingroup$ You can get "duplicate" galaxies in "ordinary" lensing, though astronomy.stackexchange.com/questions/16795/… $\endgroup$ Commented Mar 12 at 18:10
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    $\begingroup$ My diagrams are for a Schwarzschild black hole, and they show that even a small change in light ray impact parameter can give a large change in deflection angle. So the rays from different parts of an extended lensed body can experience quite different deflection. However, many photos of gravitational lensing involve an extended lensing object, which gives more complicated results. en.wikipedia.org/wiki/Gravitational_lens#Gallery has numerous examples of lensing producing multiple images of the lensed body. $\endgroup$ Commented Mar 13 at 3:35

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Duplicates of galaxies and bright point sources are seen quite often in gravitational lensing. My favorite is probably this image of the galaxy cluster MACS J0138:

MACS J0138 galaxy cluster Credit: S. Rodney (U. of S. Carolina), G. Brammer (Cosmic Dawn Center), J. DePasquale (STScI), P. Laursen (Cosmic Dawn Center)).

The image on the left is from 2016, and the image on the right is from 2019. The big, reddish arcs that encircle the cluster are multiple images of the same background galaxy (MRG-M0138): one on the right side of the cluster, and two that are smeared out over each other below the cluster. A fourth image is seen as a radial arc closer to the center at ~22:30 o'clock.

The reason I like this example is that a supernova ("SN Requiem") exploded in the background galaxy, and appeared in three different locations in 2016. They were discovered a bit by chance by my colleague (who has good eyes), when he noticed that the three dots had disappeared in 2019.

Because the light takes different paths around the cluster, there is typically a time delay of the order of months in such cases. By modeling the mass distribution of the lensing cluster, it is possible to learn pretty accurately how much the light is delayed, magnified, and distorted. Doing this, it was actually possible to predict that a fourth image of SN Requiem should appear in 2037 (± a few years) in the location marked by a yellow circle in the right image (Rodney et al. 2021).

The reason the time delay for that image is so much longer is that it's closer to the center of the cluster, meaning that the light traverses a deeper gravitational potential, meaning that time goes slower. Pretty cool, right?

Another cool example is the lensing and magnification of what we believe to be a single star, dubbed "Earendel" at a distance of 28 billion lightyears. The star itself is only seen once, but the star cluster that it's a part of is seen three times:

Earendel Credit: NASA/ESA/Brian Welch (JHU)/Dan Coe (STScI)/Peter Laursen (DAWN).

The above image is a close-up of the tiny region where Earendel happened to fall right on top of the narrow line where the magnification increases by (tens of) thousands of times (a so-called "caustic line"; in the image I called it "magnification line" because it was used for a press release). A cluster of many stars is seen slightly offset from the line, resulting in a much smaller magnification but instead being mirrored by gravity.

Do we see many?

In order for a galaxy cluster to produce multiple images of a background source, it must be rather massive, and also quite concentrated in mass. Small clusters rarely act as strong lenses, but once you get above a certain mass, say $M\gtrsim10^{15}\,M_\odot$, a large fraction of them show those giant arcs, and also multiple images of the same background object. Other famous clusters include e.g. Abell 1689 showing ~30 multiply imaged background galaxies (Limousin et al. 2007), and Abell 2744, with no fewer than 61 multiply imaged galaxies (Jauzac et al. 2015).

So yes, we see many!

Mirrors and multiple orbits of light

The illustration in the post you link to was actually made by me for a press release for a related, but physically quite different situation, discovered by Sneppen (2021). This is an analytical solution to an idealized situation where light in principle can circle arbitrarily many times around a black hole. So yes, in principle you can see arbitrarily many copies of both background objects, and in fact objects on any side of the lensing black hole, including yourself.

In order for a light ray to be deflected even just once (i.e. to make a mirror image), the trajectory of the light must be very, very close to the lens. This means that only black holes work, because all other objects are not compact enough (for extended lenses, as you approach the center you also have less and less lensing mass). That's why for galaxy clusters you always only see deflection angles of the order of arcminutes, not degrees, and definitely nothing close to 180°.

So the words "in principle" carry a heavy weight here. As you look closer to the black hole, the trajectory deflects exponentially fast. That means that an extended object will in practice be smeared out over 360° around the black hole forming a ring, ruining the (mirror) image. So no, a group of rays from a distant galaxy would in general not look like a galaxy.

There is one scenario that could perhaps work: It turns out that for rotating black holes, you do not need to look so much closer to the black hole to see the next image. For a maximally rotating black hole you only need to look at half the distance between one image and the black hole, in order to see the next image (compared to $e^{2\pi}\sim500$ for a non-rotating black hole).

So in the ideal situation that you have a fast-spinning, nearby black hole you could in principle (!) (!) see your distorted mirror image. Sort of like this illustration that I also made for the same press release (and which importantly is qualitative, not quantitative):

galaxy image distortion around a black hole

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    $\begingroup$ "The reason I like this example is that a supernova ("SN Requiem") exploded in the background galaxy, and appeared in three different locations in 2016. They were discovered a bit by chance by my colleague (who has good eyes), when he noticed that the three dots had disappeared in 2019." Good eyes indeed, holy crap. Thank you for telling this story, what an incredible find. $\endgroup$ Commented Mar 13 at 15:57
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    $\begingroup$ @GlennWillen Thanks :) Yes, software, pipelines, and machine learning can only get you so far. Nothing beats human experience (in some circumstances, and this will probably no longer be true in ten years). $\endgroup$ Commented Mar 13 at 22:17
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    $\begingroup$ @Peter-ReinstateMonica I agree, but I think we probably know hundreds of clusters with sufficient mass to each have tens of mirrored galaxies. $\endgroup$ Commented Mar 16 at 13:42
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    $\begingroup$ @adsp42 I agree, it's probably confusing to use the term "mirror image" for both multiple images and for light rays actually (but hypothetically) being reflected in the direction of the source. I guess that's astronomers for you. $\endgroup$ Commented Mar 17 at 7:56
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    $\begingroup$ @adsp42 But note that back-reflection is really only possible, even in principle, in the case of black hole, or possibly in the case of extremely compact neutron stars. Clusters are so extended that deflection angles of light from background sources is of the order 1 arcmin. It would thus take 60×180 ~ 1e4 clusters to make light do a 180° turn. Given typical distances between cluster (say, 50 Mpc) this would bring the photon outside the observable Universe. And of course, meeting 1e4 clusters is unrealistic, since a light ray typically meets only ~1 cluster on its way through the Universe. $\endgroup$ Commented Mar 17 at 8:07
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This is not common. See Einstein Cross. You end up with multiple points of light that are nonetheless recognizable as images of the same object, because they'll share a spectrum & redshift.

There're only a few Einstein crosses known, hence it's not common.

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  • $\begingroup$ +1 from me to compensate that unfair negative vote. The (early) answer is appreciated and you should be excused for not noticing some of the initial comments referring to Einstein cross (assuming that was the reason for the -1, otherwise valid answer). $\endgroup$ Commented Mar 17 at 11:39

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