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Update: Joe Kissling raised some important objections in the comments - I'll play about a bit with black hole masses and update my question accordingly - any answer along similar lines might be outdated soon.
Update 2: I'm asking for the smallest feasible MBH here.

So I want a large power source to heat my new real estate on the Jovian moons. I create a micro black hole (MBH), maybe a few kg, maybe more and drop it into Jupiter. I expect the following to happen:

  • the MBH absorbs mass and emits Hawking radiation
  • Mass falling towards the MBH will heat up due to the high pressure near the MBH
  • the MBH will find its way to the center of the gas giant
  • Hawking radiation, even hard radiation like gamma rays, will be mostly absorbed by the gas giant and be converted to heat
  • there will be no stellar fusion, as the overall pressure even near the event horizon will be too low
  • Ultimately, the gas giant is consumed

My question is,

  • Are my assumptions above what will happen wrong?
  • how long will all of that take (how long till the gas giant heats up noticably, how long til its gone)?
  • how hot will my gas giant become (will it remain an infrared source or become hot enough to shine in visible light)?

I hope for reasonable back of the envelope calculations or reasoned arguments

P.S.:
Strangely, the only fictional treatments of MBH as power source I recall are from Charels Stross (Singularity Sky, Iron Sunrise) and Karl Schroeder (One of the Gennady short stories) and none involeved a gas giant. But I'm somehow pretty sure that MBH meets Gas Giant has been done in fiction, and maybe the author did some math to back it up - maybe an avenue for research? I just don't know where to start.

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    $\begingroup$ Your assumptions are wrong. The MBH will be too small to absorb mass, the outflow of radiation will also keep it from even reaching the event horizon. At a mass of a few kilograms, it won't accrete mass and will probably evaporate so rapidly as to be indistinguishable from a nuclear explosion. The gas giant will not be consumed and will hardly be affected at all. $\endgroup$ – Joe Kissling May 10 '17 at 6:29
  • $\begingroup$ You are correct that a singe digit-kg MBH will evaporate in ~10E-17 seconds (which I hadn't grokked when writing this q), but the calculation for evaporation time (in the hawking radiation link) is based on the assumption that there's no mass nearby to absorb, no? Else it wouldnt make sense. $\endgroup$ – mart May 10 '17 at 6:38
  • $\begingroup$ At that mass how would it attract other matter to it? Your monitor or laptop has a mass of a few kilograms, how fast are you currently falling towards it? At that scale, the event horizon of the black hole would be too small, and you still have the outpouring of radiation to go against. $\endgroup$ – Joe Kissling May 10 '17 at 6:41
  • $\begingroup$ I shoot it into the mass (even so it might not work out). You already convinced me the single digit kg won't cut it, ~1000t is the lower bound (then liftetime would be measured in seconds). $\endgroup$ – mart May 10 '17 at 6:46
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    $\begingroup$ Can't access your link now but will do so. $\endgroup$ – mart May 10 '17 at 6:54
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Black Holes are not the vacuum cleaners of space. A BH of a couple kg would do nothing, it would evaporate.

As a bad analogy, if you stand in your room, try to grab a pencil that is in another city. You can't, it's way to far away, and also you're exploding really fast.

Even if it was ~1000t and had a lifetime of 80 seconds, it has a radius of $10^{-12}$ nm. The distance of two atoms/molecules in an ideal gas is roughly 3 nm. So how much matter could it meet?

Let's say it's travelling at light speed (it would be way slower, relativity and all).

At a lifespan of roughly $80$ s it would travel \begin{equation} 80 s\cdot 300000m/s = 2400000 m \end{equation} before it would perish. If in an ideal gas there is a Molecule roughly every $3 nm$ it would meet around \begin{equation} 8\cdot 10^{15} \end{equation} molecules which it could absorb (it wouldn't absorb anything it doesn't directly hit due to radiation pressure, speed etc).

Let's say we have a lot of Nitrogen gas, which weighs around $28 u$ or $44.8\cdot10^{-27}$ kg per molecule.

That would mean in it's 80 s lifespan it would absorb a total of \begin{equation} 8\cdot10^{15} mols \cdot 44.8\cdot10^{-27} kg/mols = 3.5 \cdot 10^{-10} kg \end{equation}

Which is not nearly enough to replace the 1000 t mass it has lost in that time. And this is a highly optimistic estimate.

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    $\begingroup$ This is a hard science question. Putting the words 'my guess' in a hard science answer is an open invitation to the delete queue. It is possible to prove, using equations, that the radiation output from a small black hole will exceed any force pushing/pulling mass into the hole. If you aren't doing that, you aren't answering the question. $\endgroup$ – kingledion May 10 '17 at 12:40
  • $\begingroup$ It's not only possible to proof, but also extremely easy. But just adding a hard-science tag to a question doesn't make it a legitimate hard-science question. I'll nonetheless will provide some numbers to back my claim. $\endgroup$ – Fl.pf. May 10 '17 at 12:52
  • $\begingroup$ If it is not a legitimate hard-science question, then you shouldn't be answering it :) $\endgroup$ – kingledion May 10 '17 at 13:24
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    $\begingroup$ meh I probably shouldn't, but I was bored $\endgroup$ – Fl.pf. May 10 '17 at 13:30
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    $\begingroup$ Black holes don't collapse, they evaporate. Its event horizon is also smaller than an atom so it won't be able to easily consume something larger than that, much less 5 other atoms around it. Especially at relativistic velocities, it will could only consume what it directly contacts. But that is a moot point anyway because the outpouring of radiation is like a continuous nuclear weapon, no matter could even get close to it, not even the pressure at the core of the sun would be enough. $\endgroup$ – Joe Kissling May 10 '17 at 14:18

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