Einstein Rings from Light Flash at Black Hole

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.


Contributed by: Thomas Müller (March 2011)
Open content licensed under CC BY-NC-SA



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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.