It's not hard for a black hole to have a smaller Schwarszschild Radius than the wavelength of commonly existing electromagnetic radiation, such as a visible light, infrared, or microwave photon.
What happens if such a photon "hits' a black hole?
Is it eaten? Somehow "partially" eaten? Not eaten? Impossible to say without a theory of quantum gravity? If it isn't eaten, is it refracted at a sharp angle?
One can study this problem as the classical scattering of an electromagnetic plane wave in the curved spacetime of a black hole. This approach involves something called the Teukolsky equation, which describes perturbations of massless fields of spin 0, 1/2, 1, and 2 around a rotating black hole. Basically, there is an absorption probability that the photon is “eaten” and a scattering probability that the photon is deflected through various angles, including sharp ones.
In the case of a rotating black hole, there is an interesting effect called super-radiance where an electromagnetic wave can scatter with a larger amplitude than it comes in with, extracting rotational energy from the hole.
We do not know of any black holes smaller than the wavelength of visible light, infrared, or microwaves. Such small black holes are only theoretical. However, a stellar black hole can be small compared with some radio wavelengths.
Within the existing theory of particle physics, the photon is an elementary particle and thus has a quantum mechanical probability to exist at an (x,y,z,t) which is given by its wavefunction mathematically represented with the same frequency as the classical wave it would build up if there were a zillion of same frequency photons.
This can be experimentally seen in this classroom experiment. The footprint of the photon in space is seen on the left hand side of the image, while the accumulated probability shows the frequency effects.
Thus a low energy photon has a probability of hitting a small black hole, and when it does, the hole will eat it up, the way the screen eats up the photons hitting it. The lower the energy the smaller the probability, because the wavefunction, is spread out in space, that is the difference the energy/frequency makes, the small $ΔV$ in space time of a small black hole is the reason.
Effective gravitational quantizations would give the same result. What will happen when gravity is definitively quantized will be seen in the future, but I suspect that the answer would be the same.
The black hole will go trough the photon wave.
If the black hole does not go through the "center" of the photon wave, then the photon and the black hole get deflected. Deflection usually involves some change of kinetic energy.
We know absorption can not happen, because if the black hole could be absorbing many photons with large wavelength while emitting few photons with short wavelength, then the second law of thermodynamics and the conservation of information would be violated.
(Hawking radiation from a small black hole consists of high energy photons)
One kilogram of incoherent photons with large wavelength contains a lot of entropy and information.
A black hole with a mass of 1 kg contains a small amount of entropy and information.
A black hole with large mass can increase its entropy by a large amount by absorbing a small amount of mass, so a particle with a small mass and a large entropy can be absorbed by a large black hole. But not by a small black hole.
