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There are many lenses that do all sorts of things. eg. horshoe lenses twist light, meta material lenses can boggle the mind.

Is it possible to make an optical lense that is an analog to a gravitational lense?

Jitter
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    Well, yeah. The answers to your earlier question plus the usual thin-lens math should point you in the right direction. You build lenses that are "wider" than spherical. Grinding them would be a bear, of course. – dmckee --- ex-moderator kitten Jan 02 '14 at 07:44
  • Actually, spherical lens have a little aberration that way in the first place, because the perfect thin lens is parabolic. – dmckee --- ex-moderator kitten Jan 02 '14 at 07:47
  • Would I get two extra images like we see in pic of the day space pictures? – Jitter Jan 02 '14 at 08:09
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    Perhaps more interesting of an optical lens is a (non homogeneous) medium with an effective refractive index similar to that of a gravitational field. It has been realized by a Chinese team some months ago. You can read the article on Nature Photonics or the e-print on arXiv. – giordano Jan 02 '14 at 21:38

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Yes, it's not only possible but relatively easy. For a gravitational lens the deflection angle at a distance $r$ from the black hole is approximately proportional to $1/r$. So your lens is going to look something like a hyperboloid of revolution:

Lens

Note that the light rays are bent increasingly strongly as you approach the axis.

This type of lens has been made and a Google will find you many examples. See for example this gravitational lens simulator.

John Rennie
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  • What kind of image would a torus shaped neutron star collapse produce at the time? – Jitter Jan 02 '14 at 08:33
  • Eh? What's a torus shaped neutron star collapse? – John Rennie Jan 02 '14 at 08:36
  • Something was in the nees recently about a supernova that could be explained by a delayed neutron star collapse. There are many mentions of torus here http://www.google.com/m?hl=en&gl=au&client=ms-android-samsung&source=android-launcher-widget&q=neutron+star+collapse+torus I will try to find the article that I read. – Jitter Jan 02 '14 at 08:49
  • I still can't find my ref to neutron stars but here is one for the asymmetric collapse of merging black holes http://arxiv.org/abs/gr-qc/9905039 forming a torus. – Jitter Jan 02 '14 at 14:34
  • The paper describes a transient toroidal structure formed during black hole merger. This isn't my area so I can't judge the paper. Maybe you need to ask a fresh question about it. – John Rennie Jan 02 '14 at 16:48
  • I have taken up your suggestion, you can find it here http://physics.stackexchange.com/questions/92224/gravitational-lensing-image-from-merging-black-holes – Jitter Jan 03 '14 at 14:44