# Can light be trapped in orbit?

Could rays of light be ever trapped in a constant orbit around a black hole if approached from a certain angle ? Like light hitting a glass or liquid with critical angle.

• Yes, this is referred to as the photon sphere. – Jack Moody Mar 19 '18 at 21:08

In principle yes, but in practice no.

At the so-called photon sphere, gravity is exactly so strong that a photon on a tangential trajectory would stay in orbit. For a non-rotating black hole of mass $M$, the radius of the photon sphere is $3/2$ times the radius of the event horizon — i.e. the "surface" of the black hole — which itself is given by $r_s \equiv 2GM/c^2$, where $G$ and $c$ are the gravitational constant and the speed of light, respectively.

However, the orbits are unstable; any perturbation will cause a photon on the photon sphere to either escape or plunge into the black hole.

• I think the problem is that you can't enter that orbit from a different trajectory. Just as an asteroid from very far away (not part of the solar orbiting items) can only pass the sun on a parabolic or hyperbolic path, I submit that a distant photon can't be "trapped" into an elliptical orbit. – Carl Witthoft Mar 20 '18 at 15:44
• @CarlWitthoft You could emit the photon from an atom falling toward the BH, exactly at the photon sphere, tangentially hereto. A perturbation may cause the photon to escape. Time reverse, and you have a photon coming from far away, getting trapped in the photon sphere. Obviously, that requires a perfect setup, but it's physically possible. – pela Mar 20 '18 at 16:50