Einstein Rings from Light Flash at Black Hole

scaled position x

0.2

number of orbits

1

2

3

position r	=	10.
current values
critical angle	=	27.6946°
Einstein angle	=	27.9935°

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

ξ

. 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,

x=

r

s

/r

, where

r

s

=

2GM

2

c

is the Schwarzschild radius of the black hole,

G

is Newton's constant,

M

is the mass of the black hole, and

c

is the speed of light. The radial coordinate

r

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.