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What effect does the size of a black hole have on the size or density of the photon sphere and it's proximity to the horizon?

For example: A person is in space looking at 2 black holes, one of them big and the other small. Could the bigger one appear smaller because of the way space bends around it?

If yes, can a large enough black hole be completely hidden behind the gravitational lensing? Could a dense photon sphere around a black hole look like a spherical distortion to distort the horizon or hide the black hole completely?

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    $\begingroup$ What do you mean by a "naked black hole"? $\endgroup$ – antispinwards Feb 16 '19 at 9:51
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    $\begingroup$ @mistertribs Given the OP description of the scenario I believe a "naked black hole" is a black hole without an accretion disk. I'm not sure I fully understood the question but the "size you see" depends on your position and the lensing effect since it is given by the photons that reach (or not) your eyes. Likely the perceived "size" of the black hole would increase dramatically as the distance to it decreases (much more so than a "normal" object like an equally sized planet). But take this as an informal opinion, I'm not an astrophysicist. $\endgroup$ – armatita Feb 18 '19 at 15:24
  • $\begingroup$ @armatita this would make a good answer. I'm asking can the photon sphere of a larger black hole may appear larger while the black hole itself would appear smaller? $\endgroup$ – Muze the good Troll. Feb 18 '19 at 16:45
  • $\begingroup$ @Muze I don't wan't to given an answer because I'm not knowledgeable enough about the subject to avoid (a lot of) speculation. In any case, you say "appear" so I'm assuming you wan't to know what happens when an external observer is looking (with eyes, cameras, etc.) at the black hole. I would assume the dark patch to be the photon sphere and not the event horizon. As so from the outside you wouldn't be able to tell the difference. In the photon sphere you would not see light coming from below. After that the dark starts to cover more and more of the sky as access to photons becomes scarcer. $\endgroup$ – armatita Feb 18 '19 at 17:32
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    $\begingroup$ @Muse for you first question I believe that the photon sphere should increase as the black hole increases with size. Photons are massless so I'm not sure what you mean by density. Generally the photon sphere maintains a constant distance to the even horizon. See Wikipedia for the calculations. $\endgroup$ – Max0815 Feb 22 '19 at 2:26

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