|MadSci Network: Astronomy|
I think this is a terrific question, but then again I might be biased because you've hit upon the topic of my PhD thesis...gravitational lensing! One of the implications of Einstein's theory of General Relativity is that matter can exert a gravitational force on light and `bend' it. Another way of thinking of it is that a very massive object can actually warp the spacetime around it (think of an elephant sitting on a mattress), causing any photons traveling nearby to be deflected from their original paths.
In fact, this was one of the earliest experimental tests confirming the predictions of relativity. In 1919 the famous British physicist Arthur Eddington traveled to an island off the coast of Africa to take photographs of a a total solar eclipse. When he compared the location of the stars very close to the Sun and made visible by the eclipse, he found that they had been deflected from their normal 'unlensed' position. This was great experimental confirmation of what was then still a revolutionary new theory.
The effect of one star lensing another star (called 'microlensing') is now routinely observed by teams of astronomers who continuously monitor millions of stars. While they can't hope to resolve the extremely small angles they do look for a characteristic brightening and dimming of the background star and from this they can determine the mass or 'weigh' the lensing star!
But weird lensing effects don't stop there. You asked about a star appearing in two places at once -- while a single star acting as a lens isn't massive enough to bend light from another star enough to split it into multiple images, there are objects in the universe massive enough to do that: galaxies, and clusters of galaxies. In this way we get a gallery of wacky objects that have been magnified, stretched or split by a foreground lens. If two galaxies are perfectly aligned you see an Einstein ring; if they aren't perfectly aligned you get muliple or distorted images. Best of all (in my opinion) if you look through a massive cluster of galaxies you see a whole zoo of distant background galaxies that have been stretched into giant arcs.
Gravitational lensing is important for two reasons (aside from generating pretty pictures!). Firstly, since the lensing effect we observe (the magnification or distortion of the background galaxy) depends on the mass of the lens, it allows us to directly determine the mass of the lens...and that means we can map out the 'dark matter' that makes up so much of the universe, even if we can't see it directly. Secondly, the lens acts as a giant 'gravitational telescope', magnifying distant objects and allowing us to see even further and deeper into the universe.
Finally, in answer to your second question, since the angles involved in lensing are so small it's unlikely that any gravitational lens could turn light back on itself so that we could see the far side of a star or other object. But it does mean we can sometimes see around objects, as in the case of the Einstein ring above!
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