Re: Blackhole Engines, again.

Logan Kearsley wrote:

Let's say you've got two micro-blackholes, massing a total of 9560 tonnes
(why that mass? because I felt like it).
Normally, they'd decay in about 9180 seconds, but orbiting them around each
other gives you the benefit of time dilation. Say that you orbit them
separated by five times their diameters (just to give a large safety
margin), the combined time dilation effects of their orbital speed and being
in each other's gravity wells slows that a little bit to 10200 seconds (~2.8
hours), more if they orbit closer, less if they orbit farther (at the
closest possible orbit, just before they merge, time-speed is about halved,
assuming that the time dilation effects should be multiplied rather than
added [?]).

The equations involved here are

P = K/m^2

tau = [c^2/(3 K)] m^3 = K' m^3

where m is mass, P is power, tau is lifetime, and

K = 3.563 x 10^32 W kg^2

K' = 8.408 x 10^-17 s kg^-3.

For m = 9.560 x 10^6 kg, P = 3.899 x 10^18 W, and tau = 7.346 x 10^4 s.

Assuming I haven't made any calculation errors, the power rate is about
3.11976e19 Watts, and the fuel injectors have to be able to supply
~937.25kg/s just to keep the holes from decaying, plus reaction mass. Not
too challenging, I think. The mass flow, that is- controlling that much
wattage will be difficult.

That's incredibly difficult, actually. Think about it. The Schwarzschild radius of a black hole with a mass of 9560 t (R_s = 2 G m/c^2) is 1.420 x 10^-20 m -- far smaller than a proton. That means the only way you can feed it is with pointlike particles. Your best choice is probably an electron, since it's pointlike, charged and thus easily manipulable because of its charge, and stable. But to maintain equilibrium, you need to feed it the mass energy equivalent of its total power. At 3.899 x 10^18 W, that's 43.78 kg/s. That doesn't sound like much, but you're feeding it that in electrons. That means you need to get 4.806 x 10^31 electrons every second into a black hole. But that black hole is emitting Hawking radiation at an incredible rate -- that is the whole point, after all -- and somehow the electrons have to get through that and reach an object smaller than any subatomic particle.

But that isn't even the half of it. Those electrons are charged, and so when the black hole swallows them, it too will become charged. There are Hawking-like processes that dissipate electric charge, but of course they do it by emitting charged particles. So no matter how fast that process takes, the black hole and/or the region right it is going to have enormous negative charge. But you still have to keep firing electrons in there to feed it, and like charges repel, so you're going to have to crank up the energy on the electrons you're firing in, causing you have to expend more energy just to maintain equilibrium.

Let's not forget, also, that the Hawking temperature of the black hole is going to be 1.283 x 10^16 K, which in terms of particle energy is 1.772 x 10^8 J = 1.106 x 10^27 eV! Thus, the Hawking radiation itself is going to consist of all sorts of exotic particles, many charged (albeit in equal numbers) which will seriously impair your ability to feed the hole. The process becomes even harder if there is more than one hole in some sort of orbit around each other. (And then there's gravitational radiation ...)

In short, it strikes me as the kind of idea that's easy to write down on paper, but it seems practically utterly impossible to realize even with near-magical technology. Now, if you're just talking about capturing a primordial black hole and collecting its Hawking radiation until just before it evaporates, then that makes sense. But actively trying to maintain equilibrium with a black hole that is small enough to be emitting significant amounts of Hawking radiation seems extremely farfetched to me.

--
Erik Max Francis && max@xxxxxxxxxxx && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis
The eternal silence of these infinite spaces frightens me.
-- Blaise Pascal
.

Relevant Pages

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