To repeat what I just posted: what form does the use of mechanics to determine if the character knows about trolls take?IMO there is a significant difference between using the mechanics to determine if one's character knows about trolls, and another in which the player uses their knowledge about falling damage and their current hit point total to inform themselves if their character can survive jumping off a 40 foot height before their action declaration. The latter I would classify as metagaming, not the former.
Is it an action declared by the player for the PC (eg "I rack my brains to recall everything I ever heard about trolls!")? Then it is author stance: the player wants to be able to beat the trolls, apprehends that some in-fiction knowledge must be established, and declares an appropriate action. (And easily retrofits a PC motivation - I don't want to be eaten by trolls!)
Is it a check called for by the GM? Then it involves no stance on the player's part, as it's not an action declaration.
Either way, it might establish some fiction - eg that the player knows about trolls, or is ignorant of them - which can then support further actor stance action declarations. But it, itself, is never going to be actor stance as far as I can see.
(Btw, my understanding of orthodox 5e D&D is that the GM doesn't call for knowledge checks in the absence of a player action declaration, so that only the author stance version of a knowledge check can occur. If that's a correct account of 5e, it clearly marks a difference between 5e and some earlier editions, such as AD&D, B/X and 4e.)
What aboutusing knowledge about falling damage and current hit point total to inform a character's decision to jump off a 40 foot clilff? If that mechanical knowledge corresponds to some character mental state then this can easily be done in actor stance. (I assume most D&D players assume that the player knowledge that a sword does d8 damage and a dagger does d4 damage corresponds to character knowledge that swords are more dangerous than daggers. Presumably, then, at some tables the falling damage rules are taken to work the same way.)
If the player's mechanical knowledge does not correspond to anything that is in the character's mind, then this can't be done in actor stance.
I would add: because the relationship between hit points, damage and the fiction is quite flexible in D&D, there are a range of possible character mental states that are in play here. For instance, in 4e I wouldn't assume that the character in this scenario knows s/he will survive. Rather, I would assume that the character reasonably hopes that s/he will survive, and jumps of the cliff in part motivated by that hope. Thus I would say that a player decision that his/her PC jumps could easily occur in actor stance: the action declaration issues from a combination of the character's knowlege/beliefs (there's a 40' cliff; at the bottom of the cliff there are orcs attacking the villagers; I can only help the villagers by getting to the base of the cliff), expectations/hopes (Bahamut's got my back) and desires/commitments (I need to helpf those villagers).
If a table uses D&D-ish hit points, but doesn't allow for character mental states like Pelor's got my back that correlate to having a good hp total, then actor stance in this sort of case becomes much harder. In B/X, for instance, and in Gygax's DMG, hp seem to underlie a pawn stance approach. (This is another instance, in my personal opinion, of 4e taking these classic D&D-isms but really running with them in ways that classic D&D didn't envisage.)