4
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Yes, this is referred to as the photon sphere. $\endgroup$ – Jack Moody Mar 19 '18 at 21:08
9
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ 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. $\endgroup$ – Carl Witthoft Mar 20 '18 at 15:44
  • 1
    $\begingroup$ @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. $\endgroup$ – pela Mar 20 '18 at 16:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.