system
Given the following post, respond as if you're commenting on Reddit:
human
Black hole = magic refrigerator?

Assume I have a large black hole.

And that I have an environment that is extremely hot due to photons flying everywhere.

Let's say I build a giant machine to transfer those photons into the black hole. Not just in the immediate vicinity, but across a vast area.

My question is, is there any limit to how large a machine the hole would be able to cool off by having the material transfer heat into it via radiators or similar. Like, if I built a machine much larger than the actual event horizon that is meant to pass heat into the hole, is there any reason in particular I can't cool the entire machine to the temperature of the hole? Like can I essentially use it as an unlimited thermal wastebin that gets colder and bigger the more heat I throw in it?
gpt
Yes. This is ok. Black holes are actually magic refrigerators. Since, as you note, they have negative heat capacity, you can keep on dumping heat and they will only get colder, not hotter.

However, if what you need is to lose heat, you can just use empty space. Empty, flat space is at a temperature of absolute zero. You can radiate away all you want and its temperature will always stay zero: it has infinite heat capacity.