What happens when you shine circularly polarized light at a pole of a rotating black hole?

Question

Circularly polarized light carries spin angular momentum (SpAM ), so shining it into a pole of a spinning black hole from a point on the rotation axis of the BH should raise the angular momentum of the latter. Moreover, the magnitude of a photon is constant at 1 ℏ while its energy can be arbitrarily low. So light can carry arbitrarily high SpAM per unit energy. Thus, it should be possible to wield circularly polarized light to put angular momentum into a BH with arbitrarily high efficiency. So, could we make a naked singularity by shining circularly polarized light whose frequency is low enough at the pole of a rotating black hole in parallel with the rotation axis of the BH?

Or would the long wavelength of such light cause problems, e.g. due to the Uncertainty Principle (though this principle is just an artefact of our lack of knowledge of the precise particle positions according to Bohmian Mechanics)?

Light can also carry orbital angular momentum (OAM). Could we use that, too, to raise the angular momentum of the BH? I have a feeling this might be problematic because OAM needs (does it?) the light beam to have breadth, so it wouldn’t be possible for the whole beam to perfectly hit the pole, wherefore the rotation of the BH might somehow prevent such light from coming in. Is that correct?

Answer 1

In reality there is no such thing as a beam of light travelling exactly along the symmetry axis of the spacetime. Any wavepacket needs to have a finite size.* For any finite size wave packet the Sorce and Wald theorem (discussed in this answer) states that it is impossible for a packet with sufficient angular momentum to energy ratio to ``over spin'' the black hole to actually hit the black hole.

The physical mechanism preventing it in this case is spin-spin interactions between the BH spacetime and the wavepacket causing it to be deflected/dispersed before entering.

*) From a quantum mechanical point of view this is just the uncertainty principle. The direction $\phi$ and impact parameter $b$ are non-commuting observables, hence if you perfectly fix the direction the light is coming from you have infinite uncertainty in the width of the beam, and vice versa.