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I read somewhere that gravity is able to bend light.

Is there a chance that, if the conditions are right, the light from one star could bend so much through space that when it reaches the telescope we use to look at it, it could actually be behind us?

As an analogy, imagine you have a piece of rope (the light) and every time it goes past an object that has gravity it bends a tiny bit, in the end it has made a 180* turn and is traveling back to the point it started.

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    $\begingroup$ If somehow you reach the event horizon of a black hole ( where the light is in orbit) you can see the back of your head in front of you $\endgroup$ – Shashaank Mar 1 '17 at 14:56
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    $\begingroup$ @Shashaank that, with some more discussion and details, could be a good answer $\endgroup$ – DilithiumMatrix Mar 1 '17 at 15:01
  • $\begingroup$ @DilithiumMatrix Ok I will try my best ! $\endgroup$ – Shashaank Mar 1 '17 at 15:01
  • $\begingroup$ @DilithiumMatrix I have tried but I am still a beginner at the Maths of GTR so I have avoided it . Please see if there are any faults and suggest correction because I was quite doubtful regarding time dilation effects at even horizon affecting the sight of observers back . $\endgroup$ – Shashaank Mar 1 '17 at 15:20
  • $\begingroup$ Dr. Suess, "The Big Brag" ;-) $\endgroup$ – user129544 Mar 1 '17 at 19:54
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For the 1st paragraph of your question:

You need light to see anything.

Firstly I will emphasize on my comment.

If you reach the event horizon of a black hole safely (where light can get into orbit around the black hole), then since the light is in orbit, the light from the back of your head would go around the black hole and come back to reach the front of your eyes enabling you to see the back of your head. But there are subtleties involved and I am just a beginner in general relativity.

Secondly for your question. It does happen. It's called Gravitational Lensing.

A gravitational lens is a distribution of matter (such as a cluster of galaxies) between a distant light source and an observer, that is capable of bending the light from the source as the light travels towards the observer. This effect is known as gravitational lensing, and the amount of bending is one of the predictions of Albert Einstein's general theory of relativity.

In general relativity, light follows the curvature of spacetime, hence when light passes around a massive object, it is bent. This means that the light from an object on the other side will be bent towards an observer's eye, just like an ordinary lens. Since light always moves at a constant speed, lensing changes the direction of the velocity of the light, but not the magnitude.

From Wikipedia:

Light rays are the boundary between the future, the spacelike, and the past regions. The gravitational attraction can be viewed as the motion of undisturbed objects in a background curved geometry or alternatively as the response of objects to a force in a flat geometry.

$\theta = \frac{4GM}{rc^2}$

toward the mass M at a distance r from the affected radiation, where G is the universal constant of gravitation and c is the speed of light in a vacuum.

Have a look at this:

https://en.m.wikipedia.org/wiki/File:Black_hole_lensing_web.gif

Incidentally, Gravitational Lensing is used widely to predict the existence of dark matter and gravitational lensing has shown that the dark matter problem isn't due to a fault in GTR (I have read so) or due to its incompleteness but rather the Standard Model is incomplete (once again, Einstein prevails).

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    $\begingroup$ You don't need to get all the way to the event horizon -- the circular photon orbits are at radius $\frac32$ times the radius if the event horizon. So there does not even have to be a black hole: the Schwarzchild space outside a sufficiently massive neutron star will allow you to see yourself from behind. (Were it not for the fact that its gravity would smash you flat before you could get out your telescope, of course). $\endgroup$ – Henning Makholm Mar 1 '17 at 17:24
  • $\begingroup$ @HenningMakholm A rotating neutron star indeed. I am a beginner at GTR $\endgroup$ – Shashaank Mar 1 '17 at 17:58
  • $\begingroup$ @HenningMakholm - actually the gravity would pull you apart. Your center of gravity will be travelling in freefall in orbit, but the parts of you closer to the star would experience tidal forces pulling it closer, while those farther away would experience the opposite tidal forces. $\endgroup$ – Paul Sinclair Mar 1 '17 at 18:04
  • $\begingroup$ @PaulSinclair: I'm imagining standing on the (non-rotating) neutron star. At the point we're talking about, it is impossible for things with rest mass to be in a stable orbit anyway. $\endgroup$ – Henning Makholm Mar 1 '17 at 18:06
  • $\begingroup$ @PaulSinclair I understood it till the time I saw Cooper fall into the Tesseract ! $\endgroup$ – Shashaank Mar 1 '17 at 18:07
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Yes in principle that is possible, however usually you won't recognize the light as a star anymore, because it has to come very close to a large gravitational field of a black hole. What is indeed observed and you can find pictures of that is black holes acting as gravitational lenses so that you see galaxies or stars behind it multiple times. This is possible because the light can bend around the black hole on different sides. So if you are just looking for the effect of gravity bending light I suggest looking for that.

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