Throttling a black hole engine?

Question

So, building artificial black holes is Really Hard. And when they get too small, they go out in a Really Big Dangerous Bang.

Thus, if you manage to build, e.g., a kugelblitz factory that produces mini-black-holes with gigawatt-scale Hawking power output as starship / space station power plants, it seems to me that, rather than using them as one-off batteries, it would be nice if you could maintain your tamed black hole in a steady state, consuming matter at the same rate as it emits energy. And it'd be even better if that rate could be controlled.

A Very Long Time Ago (I think back when I was still on rec.arts.sf.science), I worked out a scheme where a pair of orbiting black holes could be used to provide throttled output with high responsiveness injecting angular momentum into the system to widen or contract their orbit, thus decreasing or increasing the level of time dilation each experiences as a result of the other; however, I am no longer really optimistic about that approach, because

1. Interaction cross-sections are really low, so injecting angular momentum turns out to be really inefficient, and
2. Interaction cross-sections are low, so you can turn the output up and down, but you can't really maintain a steady-state operation for anything that has a conveniently high power density. The output radiation will produce too much pressure to let anything else back in.

More recently, having researched those interaction cross sections, I've been contemplating the possibility of embedding a micro-black-hole in a shell of degenerate matter. Neutron star atmospheres are only about 10cm thick, and that provides enough pressure to stabilize "frozen plasma" degenerate nuclear matter in the crust, so a structure only a few meters wide consisting of gravitationally-confined hydrogen plasma confining neutron-star material ought to work. This kind of system can be maintained in a steady state at megawatt or gigawatt outputs, but it's balanced on a knife edge: don't feed it enough fuel to keep the pressure up, and the black hole will start emitting more than it consumes, getting into a positive feedback loop that eventually blows everything up. But feed it slightly too much, and the black hole will eat too much, which will lessen its output, which will reduce the stagnation pressure and allow it to eat faster, and eventually your whole powerplant collapses into a larger, colder black hole.

Now, if you can come up with some way to mechanically couple to the degenerate matter shell that mediates feeding the black hole, there may be another way to control it--spinning up the structure will reduce the core pressure, reducing the capture cross-section, and spinning it down will increase the core pressure, increasing the capture cross-section, which provides slightly better control than just slowly feeding it and hoping that you never accidentally feed it just a smidgen too much. But how to actually manage that spin control is still a sticking point, and it still doesn't provide a huge range of stability.

So... ya'll got any better ideas on how to control a micro-black-hole for steady-state matter/energy conversion?

Answer 1

It seems like you're worried about a problem that's not really a problem.

Firstly, black holes take a long time to evaporate... over 575 trillion years at 6x10¹¹kg (for gigawatt luminosity), over 15 million years at 1.8x10¹⁰kg (for terawatt luminosity) and over 2600 years at 1x1-⁹kg( for petawatt luminosity).

Secondly, mass loss via Hawking radiation is slow at reasonable power levels. Power outputs will quadruple when your mass halves, but that will take ~500 billion years, ~14 million years and ~2600 years respectively. That seems more than enough time to get your money's worth out of the thing.

Thirdly, black holes with unreasonable power outputs are miniscule... about half the radius of a neutron for the one with gigawatt luminosity. Even if you did want to keep your miniature black holes topped up, the rate of mass accretion would be very, very low indeed even if they weren't blazingly hot (which of course they are). You could probably fill them up by shooting an array of high power, very short wavelength gamma ray lasers into them... sound familiar?

Clearly if you could make a kugelblitz in the first place then you might be able to keep it topped up. Making a system that efficiently captures radiated power and uses it to drive your laser array is left as an exercise for the reader.

TL;DR: for lower power output black holes, you don't need to worry about evaporation, and for high-output black holes there's no useful way to stop the evaporation by throwing mass into them.