ANOTHER black hole question

Factual Questions
1

Granted, a singularity warps spacetime around it so that the path of light is bent passing by the hole. Too close and the hole sucks up the light altogether.

But at a certain radius, for a given singularity’s mass and a light beam’s angle of attack, light falls within a narrow band which a light beam simply orbits the black hole…
not falling in nor breaking free.

After a while, wouldn’t this orbit be totally saturated with
photons?

2

This is not possible. The event horizon is the distance from the singularity at which light just barely cannot escape. That means the only place where such an orbit is possible is right on the event horizon. A photon originating outside the event horizon can lie on a path that takes it into the event horizon and oblivion, or on a path that takes it away from the black hole, but the path of the photon cannot be entirely on the event horizon.

The only way a photon could be trapped on the event horizon itself is if it is emitted exactly on the event horizon itself. I’m a little unclear on this part, but I don’t believe this can happen because time stops at the event horizon, so no normal physical process like emitting a photon can occur. If it’s not that, then some other weirdness of the event horizon will make it OK. I think. I dropped out of General Relativity.

3

Theoretically. There’d be a “gray area” where the photons would be “orbiting”, but would actually just be falling closer and closer (like, a billionth of a nanometer) each time around… and the closer they get, the faster they fall…

Anyhoo, even if the orbit were saturated with photons, we wouldn’t be able to “see” it, because none of the photons would be reaching our eyes. Although I imagine it could be possible for a photon to be “knocked” out of the gray area (Hurrah! Freedom! Nevermind…) by a passing particle, which could just be skirting the edge of the event horizon itself, and its gravity could theoretically give a photon that needed “bump” to escape the event horizon altogher. But I wouldn’t orbit around a black hole waiting to see that happen.