When you consider that conventional chemical rockets extract a mere 10^{-8} of the energy locked up in their fuel, the attraction of antimatter becomes undeniable. Could we build an engine that extracts 100 percent of the energy created by matter-antimatter annihilation? Louis Crane (Kansas State University) is dubious, pointing to problems of storage and the difficulty of making enough antimatter to get the job done.

**Black Holes as a Propulsion Option**

Working with colleague Shawn Westmoreland, Crane has been exploring a different and far more speculative option for upping the energy extraction levels. What about using black holes for propulsion? Specifically, Crane and Westmoreland ask whether Hawking radiation from black holes can power a starship, calculating that a black hole of about a million tons would be just the right size, small enough to generate the needed Hawking radiation, while large enough to survive for the duration of a century-long star crossing. Adam Crowl has written fascinatingly about this in Crowlspace.

Crane and Westmoreland’s paper on using Hawking radiation for this purpose has been kicking around on the Net for a bit, never quite making it to the top of the queue here, but Marcus Chown gives it a good look in the latest *New Scientist*, so let’s pause to examine it now. Rather than finding a nearby black hole, the two suggest using a gamma ray laser powered by solar energy to create one. The energy needed would be enormous, calling for solar panels 250 kilometers across in close solar orbit, a Robert Forward-esque engineering challenge.

**Image**: An artist’s impression of a black hole. Credit: Jörn Wilms (Tübingen) et al/ESA.

But if you could create such solar panels and let them soak up the needed sunlight to power up your black hole production facility, you’d wind up with something tiny that offered tremendous power. Says Chown:

The resulting million-tonne black hole would be about the size of an atomic nucleus. The next step would be to manoeuvre it into the focal range of a parabolic mirror attached to the back of the crew quarters of a starship. Hawking radiation consists of all sorts of species of subatomic particles, but the most common will be gamma ray photons. Collimated into a parallel beam by the parabolic mirror, these would be the starship’s exhaust and would push it forward.

**Darwinian Selection Among Universes**

Crane and Westmoreland think a starship powered this way could accelerate to close to the speed of light in a few decades, fast enough that relativistic time dilation would occur and vast distances could be crossed by human crews. Interestingly, a black hole starship like this should create gravitational waves that might be detectable here on Earth, assuming some nearby extraterrestrial civilization were using the technology. If coalescing black holes and neutron stars ought to be producing low-frequency gravitational waves, a black hole starship should leave a gravitational signature at ultra-high frequencies.

Chown does a good job with this material, and I recommend you check out his *New Scientist* article. He points to Lee Smolin’s idea that at the singularity of a black hole, new universes could be created and bud off from their parent. It stands to reason, then, that universes that are optimized for black holes are those likely to give rise to more and more such universes. And if we could make our own black holes, then life would play a role in making infant universes proliferate.

[Crane] believes we are seeing Darwinian selection operating on the largest possible scale: only universes that contain life can make black holes and then go on to give birth to other universes, while the lifeless universes are an evolutionary dead end.

His latest calculations made him realise how uncanny it was that there could be a black hole at just the right size for powering a starship. “Why is there such a sweet spot?” he asks. The only reason for an intelligent civilisation to make a black hole, he sees, is so it can travel the universe.

“If this hypothesis is right,” he says, “we live in a universe that is optimised for building starships!”

I don’t have time this morning to get into Chown’s discussion of Jia Liu (New York University), who has concocted a spacecraft powered by dark matter, but in any case the Jia Liu paper was in queue for next week, so we’ll talk about it then. Talk about living on the speculative edge — we don’t even know what dark matter is at this point! But as fun as these ideas are to kick around, they also let us roam through broad questions of cosmology and physics in ways that can provoke discussion and help us illuminate our current propulsion constraints.

Marcus Chown’s article is “Dark Power: Grand Designs for Interstellar Power,” *New Scientist* 25 November, 2009 (available online, but get it fast before it disappears behind the magazine’s firewall). The black hole propulsion paper is Crane and Westmoreland, “Are Black Hole Starships Possible,” available online.

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If as “fraction of a micron” we pessimistically assume one micron, and the density is that of water, the mass would be 1 picogram, or 10^-15 kg. At near light speed you would have E = mc^2. If a baseball weighs 0.1 kg, to have the same energy it needs to fly at v = c sqrt(m1/m2) ~ 30 m/s. Not a bad pitch.

At a smaller fraction of a micron, and a smaller fraction of c, things are even much better than that.

In thinking about this further I was wondering if you could clarify for me whether or not Pressure = Force / area applies in this case. If so I’m having trouble seeing what the problem was that I was pointing to before. I think this may be based in a conceptual misunderstanding.

What does the E=mc^2 actually tell us in the dust grain problem? Excuse me for exposing my ignorance but isn’t this something like the work required to accelerate the grain to c? Even if it were say, comparable to a truck accelerating to 60 mph wouldn’t this be nearly nothing compared to the energy being exerted by the engine?

Further, if the pressure formula applies then it would seem a picogram grain of dust spanning 1 micron wouldn’t even be able to pierce the surface tension of water at .1c.

Thanks Eniac.

Yes, E=mc^2 stands for the energy required to accelerate the dust grain to near the speed of light. And it would indeed be negligible compared to the energy the engine would have imparted on the craft to bring it up to that speed. The fact that the dust grain still packs such a wollop brings home how mind-blowingly enormous the energy required to propel the craft really is. You may realize that E = mc^2 is also the energy you get by converting the grain/craft completely into energy. Simply speaking, you have to convert mass on the order of your payload into pure energy to get it up to near light speed.

Pressure = force / area would, of course, apply. To get pressure, though, you need to know the number of particles impacting per area and time. According to

http://astro.gmu.edu/classes/a10695/note/l08/l08s019.html,

there are on average 10^-6 dust particles per cubic meter. Our ship goes nearly c, or 3*10^8 m/s. The frequency of impacts per square meter should then be 3*10^3 m^-2 s^-1. Each has a momentum of mc ~ 3*10^-7 kg m/s. Force is momentum times rate, thus F ~ 9*10^-5 N per square meter, which is a pressure of ~10^-4 Pascal, or roughly one billionth of an atmosphere. YMMV, since dust concentrations vary widely through out the galaxy.

There is an apparent disconnect between the high energy of the impacts and the low pressure they exert. This is because energy goes with v^2, but momentum, which causes the pressure, goes with v. It is best to view the oncoming ISM as an extremely thin (leading to almost no pressure), but also extremely hot gas, which by its heat is very destructive. You are faced with a weak, but blisteringly hot headwind, essentially.

The low pressure is consistent with my earlier observation that the ISM from here until a near star amounts to a layer of less than a micron (or around that) when condensed into a solid or liquid. As long as your ship is much longer than that from front to back, it will not be significantly slowed down. It may, however, be incinerated.

This brings up a potentially serious roadblock: all this energy absorbed from the impacting ISM has to be radiated away. It may well be impossible to do so at temperatures that are consistent with a solid craft. Using an energy of 900 J per particle, and 3000 particles per second per square meter, we would have to dissipate almost 3 MW per square meter. This looks to be a very serious problem. Do the Daedalus/Icarus designers have an answer to that? Perhaps I made a mistake? My, oh my…. Someone better correct me, please!

Well, I do seem to have made a mistake or two, of two orders of magnitude, but the situation still seems pretty dire. The power density (in W/m^2) of the impacting ISM dust works out to 0.5 * rho * v^3, where rho is the ISM mass density and v the velocity of the ship. For a ship going near light speed, say 0.7 or 0.8 c, we can set v = c and use a non-relativistic approximation, this should be good to within 20% or so.

As discussed before, the mass density of the dust is 10^-6 particles per cubic meter, of 10^-15 kg each, thus rho = 10^-21 kg/m^3. The power per square meter then is 0.5 * 10^-21 * 27 * 10^24 ~ 1.4 * 10^4, or 14 kW. Now, this is much better and seems almost managable. However, we did not consider the interstellar gas. That one has a mass density that is 100 times larger, and the same calculation applies, so we would be back at 1.4 MW/m^2, total.

What could mitigate this? First of all, there were some pessimistic assumptions, in particular I assumed 1 micron dust particles when it is actually “a fraction of a micron”. Better data on the ISM mass density could therefore provide much relief, to the tune of the third power of that fraction. Also, the velocity in the third power means that another order of magnitude can be gained when going only 0.3 c, rather than 0.7 or 0.8.

If the shield were a long, sharp cone, particles would impact at a glancing angle and much of the energy might not get absorbed. Finally, we can make the ship long and slender, like a train, and cover it with radiators on the sides. The shield would be extremely hot, and would probably be made from something like tungsten. The radiators would have to be very hot, too, and some major thermodynamic engineering will be necessary to transport the heat efficiently from shield to radiators along the length of the train. The good thing is that we do not need to worry about a power source to operate the ship when the engines are off, we can simply extract power from the heat flow.

In summary, it seems that the heat from the ISM does indeed limit us to gamma factors near 1 when sticking with known physics, and the Tau Zero story must be read with a good dose of suspended disbelief. On the other hand, the Daedalus project seems to survive this analysis, although perhaps it needs a redesign in shape and radiators added.

I have not covered ablation, which may be quite more serious by itself.

Eniac, wow nice. It would be interesting to see the graph of a given surface as it is accelerated toward c compared to the radiant energy from the interstellar matter imparted to it. It seems like it would be an effective source of energy for the crew and operations at least (cruising speed). But doesn’t this break some basic laws? The ship would need to exert the same amount of energy gained from the heat of the collision to maintain it’s rate.

Eniac: you should really use relativistic analysis for things like this. Presumably we are interested in what happens as seen in the rest frame of the spaceship not in the rest frame of everyone back home.

Taking m as invariant mass, total energy per particle is E=γmc², where γ=1/√(1-β²), β=v/c. This energy can be split into rest mass energy mc² and the rest is kinetic energy, giving kinetic energy per particle = (γ-1)mc²

In lab frame, spacecraft travels at constant velocity between coordinates (ct,x)=(0,0) and (x/β,x) and encounters N=ρAx particles where A is cross sectional area.

Transforming coordinates to ship frame gives (ct′,x′) = (0,0) and (xγ[1/β-β],0)

So in time t′ = xγ[1/β-β]/c the ship encounters N particles of kinetic energy (γ-1)mc² – putting this all together gives a power delivered

P/A = γ(γ-1)ρmc³

We can substitute in various values of β: for mass per particle = 10^-15 kg and rho = 10^-6 particles per m³, I get 410 W/m² at 0.3c, 24 kW/m² at 0.8c.

This contrasts with the classical version P/A = ρm(βc)³/2, which predicts 360 W/m² at 0.3c and 6.9 kW/m² at 0.8c.

Oops correction to above post, I dropped a beta in the final expression, should read

P/A = βγ(γ-1)ρmc³

The values I gave for the relativistic model are unchanged – the calculation I was using did incorporate this β despite my omission in the post.

andy: Yes you are right, I was too lazy to go relativistic. Thanks for filling that in. I am slightly surprised the relativistic version is worse rather than better, but I really didn’t have a good idea which way it would be. Note that gas is 100 times as dense as dust, and needs to be included, so you would also arrive at a few MW/m^2 at v = 0.8 c. Then again, as I said, I am probably grossly overestimating both dust and gas mass densities. It would be nice to look up what they actually are in our corner of the galaxy. Perhaps there is an interstellar freeway running through our Local Bubble, bypassing us because of the impassable Local Cloud we are in….

David: No laws broken, the energy gained from exploiting the heat would be a small fraction of the kinetic energy lost to the slowing down of the ship. Yes, I said slow down would be negligible, but that is only in comparison to the initial propulsion energy, which is enormous. If you have to put terawatts in, you are quite lucky to lose “only” a few megawatt to “friction”. The key problem is that getting rid of heat is difficult in space, and a megawatt is a very substantial amount to try to radiate.

The Interstellar Medium (ISM) is highly variable in distribution, but the dust is definitely a very minor component. Any 1 gram “space-mines” are spread fairly widely allowing enough time and space for counter-measures – I suspect a high-powered laser to ablate the ‘space-mine’ on one side to nudge it out of the way will be sufficient. The Dana Andrews paper that Paul has referenced here a few times, “Things to Do While Coasting in Interstellar Space”, has a very effective dust/particle shield which involves a thin ‘stripper’ which ionises the incoming neutrals, then a magnetic shield around the habitat (both toroidal for the best shielding) to deflect the ion flow around the crew. The incoming flux won’t be effectively thermalised in any kind of shield we might deploy, instead deflecting the ion flow seems most effective at handling the energy. Multi-layer Whipple shields at a sufficient stand-off distance would also be effective against the larger dust flux, reducing the ISM particles to a divertable ion flow.

BTW Just how did you get those greek symbols to appear? My blog is WordPress too, but they just don’t want to appear – much to my annoyance!

Adam: Thanks for the reference to the prior discussions on this forum and the Andrews paper. I don’t know if magnetic shields actually work (How strong a field does it take to deflect relativistic ions?), but it seems reasonable that this could be the solution to the problem. I do seem to recall, though, that magnetic shielding still has some formidable problems to overcome before it can be declared feasible.

I have a hard time imagining a system that can actively detect and deflect gram sized “space-mines” coming on at light speed. I am afraid with those we just have to hope we never hit them, same as we do in Earth orbit.

βγ²√

²βγ√

Adam, I am testing insertion of math symbols above: first line beta-gamma-square-sqrt; second line square-beta-gamma-sqrt. If it shows up properly after posting, it is simply insertion of Unicode characters. I’m on Windows (XP on this machine) and using the Character Map program from System Tools.

I read Brian Wang’s version of this on his nextbigfuture site, and he proposed using a particle accelerator to feed the black hole, and this would also impart momentum to the black hole. So if the particle accelerator was directly behind the black hole in terms of where we want the ship to go, both ship and black hole will travel together.

I’ve no idea if this is reasonable or not, but it sounds good!

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