Implications of Light Orbiting Black Holes

[ScientificMind]

For black holes to "trap" light, the light would need to enter into some sort of orbit, but it seems like that might have some odd implications with relativity. If light is revolving around the center of a black hole, that would mean the light waves/photons would constantly be changing directions, which would mean that, by definition, the light would be constantly accelerating. Now I know that is a little different from acceleration in terms of speed, but I know that relativity does have aspects that involve this kind of acceleration. Anyway, my question is this, what does relativity say about that aforementioned constant acceleration, and what might the effects be in that specific example

 

[Orodruin]

For black holes to "trap" light, the light would need to enter into some sort of orbit

This is not correct. The light (and everything else inside) will just decrease its r coordinate. Since your first premise is incorrect, the rest of your question is moot.

Furthermore, things affected by gravity only in GR do not experience acceleration, they are in a state of free fall. The reason things orbit other things is because of the curvature of space-time.

 

[ScientificMind]

Furthermore, things affected by gravity only in GR do not experience acceleration, they are in a state of free fall. The reason things orbit other things is because of the curvature of space-time.

I'm aware that orbit is essentially a prolonged state of free fall, but is that not in and of itself, acceleration, regardless of the cause?

 

[Orodruin]

You have to differentiate proper acceleration (acceleration that an observer experiences) from coordinate acceleration, which is simply a result of our choice of coordinates. Along a free fall path, proper acceleration is zero by definition, e.g., for a satellite orbiting the Earth.

 

[PAllen]

Note the stable circular light orbit for a BH is outside the event horizon (it is the photon sphere). You just arrange for a light source to flash at the right distance from the BH, and the light going orthogonal to line between the BH and source will orbit. From the point of view of general relativity, this path is inertial, free fall, geodesic, as straight as could possibly be. There is no proper acceleration. (Light emitted in other directions at that flash event would either escape or 'fall into' the BH, depending on whether its direction is outwards or inwards relative the the orbital direction).

So, the way relativity deals with this so called acceleration is to say that is a false statement. There is no acceleration, there is only following the straightest possible path in spacetime.

 

[ScientificMind]

Thank you both for the help in understanding this