think big caverns with no natural light.
Do you mean no daylight or no light bulbs?
I ask as most caves I've been in have no "natural" light, but a lot were lit by light bulbs.
If no light at all (non-tourist cave), then you have to make your own. One way is to set the camera up in one spot (tripod if allowed, a ledge if not) and set it on the longest time you can, then paint the scene with a light - Flash if you can. Fire it via the test button repeatedly while you wander round the space.. A torch will do if you have to. Don't forget to light the shawls etc from behind so they glow from within.
If you have lighting supplied, use that. I find exposing warmer than you "should" works better. Cave photos always seem to look better in tones of orange than with the WB "Correct" for the light source. Last time I did cave photos it was with film. I used daylight film, no filters. The shots exposed by the tourist tungsten lights looked MUCH better than the ones exposed by flash.
If you DO use flash don't forget to warn the others in the vicinity. You'll find it is difficult to helicopter someone with a broken leg out of a cave