What were the "Black Pits" the orcs referred to?

Question

When Sam was searching for Frodo and had reached the highest tier of the tower of Cirith Ungol, he heard two orcs arguing. During the orcs' argument, the orc captain, Shagrat, alluded to the "Black Pits" in the follow quotation:

'Then you must go. I must stay here anyway. But I'm hurt. The Black Pits take that filthy rebel Gorbag!' Shagrat's voice trailed off into a string of foul names and curses. 'I gave him better than I got, but he knifed me, the dung, before I throttled him. You must go, or I'll eat you. News must get through to Lugbúrz, or we'll both be for the Black Pits. Yes, you too. You won't escape by skulking here.'
_{The Return of the King, Book VI, Chapter I}

This appears to be the only reference specifically to the "Black Pits" in The Lord of The Rings. While Gimli does mention the "Black Pit" in The Fellowship of the Ring when describing Moria,

I know them and their names, for under them lies Khazad-dûm, the Dwarrowdelf, that is now called the Black Pit, Moria in the Elvish tongue.
_{The Fellowship of the Ring, Book II, Chapter III}

it seems that the "Black Pit" Gimli referred to is different from the "Black Pits" Shagrat mentioned because Gimli specified a singular "Black Pit" and Shagrat alluded to plural "Black Pits." Therefore, what were the "Black Pits" that the orcs referred to?

Answer 1

This is confirmed in Tolkiens Unfinished Index to be the

"Dungeons of Torment under Barad-Dûr".

905 (III: 182). the Black Pits - 'Dungeons of torment under Barad-dur'
_{"Unfinished index for The Lord of the Rings", in The Lord of the Rings: A Reader's Companion, p. 603}

Given that Shagrat and the orcs of Cirith Ungol were soldiers of Sauron and under his command, therefore the Black Pits Shagrat is referring to, and the ones he tells Snaga about are definitely in Mordor, and not The Black Pit that Moria is called or the pits in the Ring of Orthanc.

Answer 2

I've always taken this to mean the pits under the Barad-Dur, but that's only a plausible assumption:

A brief vision he had of swirling cloud, and in the midst of it towers and battlements, tall as hills, founded upon a mighty mountain-throne above immeasurable pits; great courts and dungeons, eyeless prisons sheer as cliffs, and gaping gates of steel and adamant: and then all passed.