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Cooling in space is a well known difficulty. There are many unpleasant consequences like no stealth in space, difficult space battles which turn into a short wars of attrition (because you have to either pack your radiators, rendering them useless, or expose them, rendering them vulnerable), and many other complications. This is not only a problem with starships, but also with planets: even Kardashev type I civilization will run into problems keeping their cool if their energy usage on one planet already makes them a type I civilization.

But what if one considers using a black hole as a heat sink?

It seems pretty straightforward to just deposit the waste heat into the black hole, which would have a negligible increase on its mass. However, this seems to be burdened with a bunch of problems which should be addressed:

• Keeping the black hole in place. They are not really objects you can simply grab and hold. But perhaps a charged black hole (Reissner–Nordström or, perhaps even better, Kerr–Newman black hole) could be held using some sort of magnetic confinement.


• Black holes of any reasonable mass and sufficiently small gravitational field in their reasonable proximity have a very small Schwarzschild radius. Therefore, some precise aiming would be required and the question is whether this is possible to do with the waste heat.


• Hawking radiation. Planets depositing their waste heat in black holes probably wouldn't suffer from this problem, but a problem would arise when trying to downsize to for spaceships. Any reasonably small black hole would emit too much Hawking radiation which would make it too hot to be of any use as a heat sink. Using a black hole temperature calculator, it is easy to see that a black hole with a temperature of cozy $300$ K will have a mass of over $4times10^20$ kg, which is almost half the mass of Ceres - plausible for planets, but not so much for spaceships (unless we are talking about something that can be easily confused for a moon). But perhaps using an extremal black hole could help since it should not emit the Hawking radiation.

Can these issues (and perhaps some other relevant key issues, overlooked in the list) be resolved to make a use of a black hole as a heat sink?

If yes, how?

I have to disagree with most of conman's points. The issues described are merely engineering challenges, not fundamental problems. And in fact, they are engineering problems that - to some extent - have already been solved.

The first thing you need is simply refrigeration. If you don't want your spaceship radiating thermal energy in every direction, then you need to pump the heat that would normally migrate out to your hull somewhere else. It is not necessary that this heat dump be cold. But the hotter it is, the more energy will be required simply to pump additional heat into it, which in turn increases how fast its temperature will rise.

Traditional heat dumps will do if you only need to hide for a short time, and then can release that heat before it gets too hot to control. But as you've noted, long-term stealth is going to be difficult. So how about a black hole? They are not a good solution for a spacecraft. Assuming that the enormous difficulties in creating and controlling one have been mastered, a small black hole would make a excellent energy source, weapon of "mass" destruction, method of propulsion, but a truly lousy heat sink.

Getting the heat into it isn't so hard as implied. You just use a refrigeration laser to cool your more traditional heat dump and focus your laser on the black hole. Difficult, but nowhere near as difficult as creation and control.

But Hawking radiation is not your friend. From the wikipedia article, the temperature of the black hole is given by $$T approx frac1.227times 10^23 textkgM K$$
You need that temperature to be at the local background temperature for the black hole to serve as a useful heat dump to keep your ship hidden. Within the solar system, that is around $40 K$, and of course much colder in deep space. But that means your black hole has to weigh on the order of $10^22$ kg, roughly half the mass of the moon. So your ship is going to have to be as massive as a planetoid, which just isn't feasible.

So forget the black hole. But note that we now have our heat caught up in a laser beam. The great thing about a laser beam is that it doesn't radiate in every direction. For stealth, this is handy - for the enemy to spot you, they have to see the beam, which is highly unlikely. And even that vanishingly small probability can be reduced if you have some knowlege of a direction the enemy is unlikely to be in.

Now the real situation is a little less rosy. Space is not empty. There are a few particles that are going to get in the way of your laser, scattering the light. If your laser is powerful enough, that scatter may be detectable at close enough a distance. You can mitigate that risk by diffusing the beam over a larger area, dropping the energy of the scattered light, but at the risk of increasing the size of the region where the laser is directly observable. It is a trade-off of near-by stealth vs distance stealth.

For a civilization, the situation is more rosy. Go ahead and squeeze Jupiter down into a black hole. As long as you don't get too close, you won't feel any worse effects than you do now. As far as radiation is concerned, the only problems are those darn meteors and comets occasionally falling in, which will give off some nasty bursts of radiation as they fall. Aim as many refrigeration lasers at it as you want. You are not going to make a difference.

But even then, pointing those lasers at the sun instead would work about as well. The lasers can easily be hotter than the surface of the sun, and serve almost equally well for refrigeration. The sun would not be bothered by this puny addition of heat, which would then be radiated back out into space disguised as ordinary stellar radiation.

Your issue is right here

It seems pretty straightforward to just deposit the waste heat into
the black hole

Unfortunately this isn't true. The problem is that heat isn't something you can just dump into a black hole. To be clear, heat is just the random motions of atoms and molecules inside substances. There isn't a way to just "move" that into something else, regardless of your black hole's ability to absorb things. For reference, if you could somehow "move" the heat around without generating more waste heat in the process, you would have invented a lossless Maxwell's Demon, violated the second law of thermodynamics, invented an infinite energy source, and won every single Nobel Prize in physics for the rest of history, all in one go.

There is only one way you could dump heat into a black hole, which is by converting it into light and sending the light into your black hole. It turns out there is a way to convert waste heat into light. It is called thermal radiation and all materials do it naturally and automatically as a result of being hot. Taking something which is hot and cooling it by allowing it to radiate its heat as light energy is of course the well known process of radiative cooling. The trouble is that when you try to use radiative cooling to cool something, the question of where the light goes is never the problem. The bigger issue is efficiency. Radiative cooling is very inefficient, so you end up creating large "fins" to increase the surface area to generate as much cooling power as possible. For example, the radiators for the active heat exchange system on the ISS are not as large as the solar panels, but are still one of the larger features on the ISS.

This all means that the limiting factor with radiative cooling isn't where you send the light - in fact, you typically don't even care about that. Sending it off into empty space is as great as any other option. The limit is your total surface area available for cooling. Putting a black hole in the mix doesn't change any of that, so it brings no benefit to your cooling system at all. In short, we're right back to the problem you are trying to solve in the first place - the only way to dump heat into black holes is by radiative cooling, and that is what you were trying to avoid in the first place. In summary:

1. There is no way to directly transfer "heat" to a black hole.


2. The only way to get heat into a black hole would be by converting waste energy into light and sending that into the black hole


3. However, the main problem that makes cooling so hard in the first place are the inefficiencies involved in converting waste energy into light


4. If you came up with a way to efficiently convert waste energy into light you wouldn't need a black hole anyway - it would be sufficient to just send it into space.


5. Therefore, a black hole cannot help with cooling at all

But what if one considers using a black hole as a heat sink?

Yes in a simplistic sense black holes do act as heat sinks. But if you want to use them for cooling the heat generated by the energy use on a planet of a Kardashev type 2 civilization they are improbable, impractical and far too dangerous. The idea seems plausible if you ignore basic physics.

The proposition ignores firstly the physics of radiation. Thermal energy will radiate isotropically, i.e., equally in all three spatial dimensions. Even a mere Earth-mass black hole (BH) will be about the size of the full spot at the end of this sentence**.** The beamed heat would have to be concentrated into an excessively narrow beam. If possible, this would be extremely dangerous. Fortunately, it's not likely.

Imagine installing an Earth-mass BH on a planet of a K2 civilization. There will be the problems of gravity. Two centres of gravity. One, say, at the centre of the planet and the other on its surface. The engineering of keeping an Earth-mass BH in pace safely would be mind-boggling. One slip and it's disaster.

It seems pretty straightforward to just deposit the waste heat into the black hole

Not so. It would take a "magic" technology concentrate thermal radiation into a beam to intersect the required BHs.

The concept starts from an apparently plausible idea: BHs can act as heat sinks. To extrapolate this notion into mass-scale cooling systems for a highly advanced civilization further up the Kardashev scale isn't workable. While it is possible to contemplate the necessary conditions to make the technology work, those necessary conditions only highlights the real problems that would have to be overcome. The trouble is they are basic physics.