# Can light of certain wavelengths stably orbit a black hole at the photon sphere?

I've recently learned that for a black hole, its photon sphere is an unstable orbit. Light either manages to escape from or fall into the event horizon, depending on how far away from the edge of the photon sphere the light is introduced.

But let's say that the wavelength of a photon is exactly equal to the circumference of the great circle of the photon sphere, and that the photon approaches the vicinity of the black hole at precisely the right angle and distance from the photon sphere such that it ends up tangentially on the surface of the sphere.

• Is it possible for this photon to form a standing circular wave at the photon sphere given that its wavelength is precisely equal to the circumference of the great circle of the sphere?
• If so, would the photon simply stay at the photon sphere, perhaps due to some quantum stability of the standing wave?
• How can we observe this or test it experimentally?

My question also applies to the case in which the circumference of the great circle of the photon sphere is a natural number multiple (n=1,2,3,...) of the wavelength of the photon. This would be similar to the quantization of electron orbits in the Bohr model of the atom, except for photons, on a much larger scale, and in the context of gravity (i.e. curved space-time).

• Good question! But bear in mind that no real black hole has a perfectly constant mass: there are always stray atoms & radiation to absorb. – PM 2Ring Nov 6 '19 at 6:09