Einstein Rings from Light Flash at Black Hole

If an observer close to a Schwarzschild black hole fires a flash of light, some light rays return back after one revolution around the black hole. These light rays form an Einstein ring with opening angle . There are, in fact, an infinite number of Einstein rings, depending on how often the light rays orbit the black hole before they return to the observer.
In this Demonstration, you can change the scaled position of the observer, , where is the Schwarzschild radius of the black hole, is Newton's constant, is the mass of the black hole, and is the speed of light. The radial coordinate of the observer is automatically calculated. The slider "number of orbits" determines how many times the light ray orbits the black hole before it returns to the observer.
Depending on the current position of the observer, a Schwarzschild black hole appears as a black disk with opening angle equal to the critical angle.


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A detailed discussion of Einstein rings from a flash of light can be found in T. Müller, "Einstein Rings as a Tool for Estimating Distances and the Mass of a Schwarzschild Black Hole," Physical Review D, 77(12), 2008.
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