Re: Blackhole Engines, again.
- From: "Logan Kearsley" <chrono.surfer@xxxxxxxxxxx>
- Date: Mon, 10 Apr 2006 23:52:29 GMT
"Erik Max Francis" <max@xxxxxxxxxxx> wrote in message
news:kOGdnXDFbssvUKfZRVn-pg@xxxxxxxxxxxxxxxx
Logan Kearsley wrote:tonnes
Let's say you've got two micro-blackholes, massing a total of 9560
each(why that mass? because I felt like it).
Normally, they'd decay in about 9180 seconds, but orbiting them around
beingother 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
(~2.8in each other's gravity wells slows that a little bit to 10200 seconds
halved,hours), more if they orbit closer, less if they orbit farther (at the
closest possible orbit, just before they merge, time-speed is about
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.
For two micro-blackholes, massing a total of 9560 tonnes, you should halve
that mass to do the calculations for just one of the holes. But for just one
blackhole with 9560 tonnes of mass, I get the same numbers you do, so I
suppose I probably haven't made any calculation errors.
NotAssuming 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.
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
Well, actually getting the mass into the blackholes, sure, but just
supplying it oughtn't to be too hard.
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.
The blackholes could eat protons one quark at a time, which helps with the
charge problem.
Granted, that doesn't do anything about the problem of getting all that mass
into a very tiny space.
It occurs to me that with the blackholes eating protons one quark at a time,
they will repeatedly gain short-lived color charge, which could contribute
to the holes' mutual attraction (thus separation, orbital speed, and net
time dilation), and thus lower the average power rate slightly.
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 ...)
Yup. Just like last time I was thinking about this, we end up having to try
to find a balance between a power rate that's low enough to be manageable
(both in terms of feeding more mass into the blackholes, and not vaporizing
the engine), and a mass that's low enough to be moved by it's associated
power rate.
This, time, however, I've also got some vague idea of control mechanisms,
and it looks to me like we want the Hawking temperature to be high enough
that a significant portion of the output is in the form of charged
particles, too. That can certainly be accomplished with much larger masses
than my randomly chosen 9560 tonne starting point, though.
(Shouldn't the number of eV's be smaller than the number of Kelvins?1.1063 x
10^12 eV. Still plenty large to produce lots of exotic particles.)
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.
Well, let's try some different numbers. How about if the blackholes are at
least as large as a helum nucleus? I just started adding zeros until I got
something in the right range, so let's play with a set of two holes with a
total mass of 9.56e12 kg (4.78e12 kg each). That's on the scale of a small
asteroid. I'll orbit them at a distance of four times their diameters, as a
baseline (they would of course move slightly closer or slightly farther away
than that to throttle the engine).
Their radii are about 7.097e-15m, a little more than three times larger than
a helium nucleus, so they can definitely swallow nucleons whole. Unadjusted
power rate is about 15.599 MW. Nuclear reactors can beat that, so maybe we
want to go a little smaller if possible, but then nuclear reactors can't use
just anything vaporizable as fuel. Unadjusted decay time is a whopping
9.1803e21 seconds. When we adjust for time dilation, we get a decay time of
1.1016e22 seconds, and a power rate of 12.999 MW. So we only have to feed
this thing 1.7356e-10 kg/s to keep it alive! *That's* a significant
improvement. I get a temperature of ~2.2126MeV, not enough to produce
protons, but plenty for electrons, positrons, and lots of gamma rays.
Electrons and positrons getting trapped in the magnetic field and
accelerated back into the blackholes ought to reduce the required mass
inflow just a bit.
-l.
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