Light that is directed towards the center of a black hole

[jaydnul]

If a beam of light is on a trajectory that is perfectly tangent to the event horizon of a black hole (or a little below tangent, allowing it to "dip" into the EH for a moment), is it possible that that photon could be pulled into a never ending orbit around the black hole? Or is the gravity too great that not even the biggest super massive black holes in the universe could achieve this?

Edit: the title is supposed to say light that ISN'T directed...

 

[Chronos]

In theory, yes. There is a region called the photosphere where a photon can orbit a black hole. This, however, is a temporary situation. The orbit is unstable and will not persist.

 

[Sorao]

If you go nearer and nearer to the event horizon, the effect of gravity gets stronger and stronger unlimitedly. So, I think, you can always find balancing radius for a photon to orbit a black hole. But, light as wave diffuses by diffraction. So, it will not last long.

 

[Sorao]

(or a little below tangent, allowing it to "dip" into the EH for a moment),

"dip" is impossible. Anything inside the EH can not go out of the EH. This is the definition of EH. Furthermore, I think, anything can not go into the EH in our (= observers far from the black hole) frame of reference because progress of the time stops there. Following link shows further discussion.
http://en.doppolaboratory.com/engli...tions/is-the-distance-to-a-black-hole-finite/

 

[mfb]

There are possible orbits for light, but they are not at the event horizon. For non-rotating black holes, their radius is 1.5 times the Schwarzschild radius.
If light comes closer than this value, and does not get deflected (with a mirror for example), it will fall into the black hole. Once light crossed the event horizon, not even a deflection helps.

A rotating black hole has different radiuses corresponding to different directions of the orbit.

 

[Sorao]

Once light crossed the event horizon,

“Kruskal–Szekeres coordinates“ shows that light can cross the event horizon. But, I think, the crossing can take place after the end of our spacetime. I calculated the time for light to reach the surface of a black hole from a certain point by simply integrating well-known equation. It went infinite. This is shown in eq. (7) in the web page cited in comment #4 above.

 

[mfb]

Just fall in together with the light, and it will be finite for you ;).
As there is no unique way to synchronize clocks in general relativity (and even if you could do this, they would run out of sync again), it is not so clear what "happens after time x" means.

 

[Sorao]

All I wanted to say is that eq. (7) seems simple enough to convince me.

 

[Superposed_Cat]

But, light as wave diffuses by diffraction. So, it will not last long.

defracts off what?

 

[tiny-tim]

the photon sphere is at radius 3M around a black hole (where the event horizont is at 2M)

close to the photon sphere, light can orbit many times before escaping

see https://www.physicsforums.com/library.php?do=view_item&itemid=268 for details

 

[Sorao]

defracts off what?

A laser pointer can spot a point sharply at a screen 10m ahead. But it can’t spot a point 100m ahead because the beam diverges and brightness of the spot decreases. This is because of diffraction. Additionally, because of strong tidal effect, the divergence must be accelerated. So, I think all photons will escape or fall into the black hole before long.