What, if anything, did you do with/about white balance under black light?
I've shot under black light only a few times, auto WB produces a result similar or same as yours here, setting a custom white balance with the black light aimed at a gray card, sheet of paper, white tee shirt or what have you produces a very different result.
Mind, I'm not criticizing how you've shot here, it's actually quite dramatic and certainly places the subject well. Just saying you will find setting custom WB interesting for sure, though the look may be on the clinical side, therefore less eye pleasing. I do think it's worth a look.
Last time I set a black light WB, I intentionally left that WB set and then shot under florescents, boy and howdy that came out wrong but sure was interesting and educational. You'll likely only do that once, but that once is worth doing.
I used auto white balance, never tried anything else. What does custom WB do? Does it make the rock less blue and more natural looking? If that is the case, I think I would prefer this blue look.