Photon Orbit Around a Black Hole: Conservation Law Effects

[Ontophobe]

Hi. Now that I understand the conservation law of angular momentum, and given the fact that c is constant, I infer that if a photon were to go into orbit around a black hole, it could only take a circular orbit. No elliptical orbits for photons, because if it were to follow an elliptical orbit, it would have to speed up and slow down in order to cover the same amount of space per unit of time. Is this correct?

Related question: Can a photon "sling shot" itself around a black hole and blueshift itself in the process? (since accelerating itself isn't an option for the photon)

 

[Orodruin]

There are no elliptical orbits for anything around a black hole. Black holes need to be described using general relativity. Already in the simplest case of the Schwarzschild metric, orbits are not ellipses.

Light trajectories around a black hole are not necessarily circular.

 

[Ontophobe]

So, parabolas, hyperbolas, and circles are kosher, but no ellipses. Correct?

 

[Orodruin]

So, parabolas, hyperbolas, and circles are kosher, but no ellipses. Correct?

Incorrect. This is also something which applies to Newtonian gravity - except circles, you can always find circular orbits simply because it is a very particular special case.