The purpose of this paper is to investigate whether it is possible to build artificial Black holes of the appropriate size, and to employ them in powerplants and starships. The conclusion we reach is that it is just on the edge of possibility to do so, but that quantum gravity effects, as yet unknown, could change the picture either way.
We discuss designs for a family of machines which would in combination realize our program. The machines are far beyond current technological capabilities. The Black hole generator would be a gamma ray laser with a lasing mass of order one billion tonnes.
Other than black hole radiation, which we study below, the only process we know of which is sufficiently energetic is matter-antimatter annihilation. This has been proposed, but there are two severe obstacles.
The first is that the efficiency of antimatter production in current accelerators is well below 10^−7 (very few collisions produce a trappable antiparticle). Thus, making enough antimatter to propel a starship would use up ten million times as much energy as our proposal. The most optimistic projections of antimatter enthusiasts do not produce an efficiency above 10^−4, so that at best our proposal is still ten thousand times more efficient.
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Make the Right Black Hole
List of criteria: We need a black hole which
1. has a long enough lifespan to be useful,
2. is powerful enough to accelerate itself up to a reasonable fraction of the speed
of light in a reasonable amount of time,
3. is small enough that we can access the energy to make it,
4. is large enough that we can focus the energy to make it,
5. has mass comparable to a starship.
A black hole with a radius of a few attometers at least roughly meets the list of criteria. Such BHs would have mass of the order of 1,000,000 tonnes, and lifetimes ranging from decades to centuries. A high-efficiency square solar panel a few hundred km on each side, in a circular orbit about the sun at a distance of 1,000,000 km, would absorb enough energy in a year to produce one such BH. The family of BH solutions has a “sweet spot.”
Four Machines for Implementation
These devices are far beyond current technology, but we think they are possibly capable of being implemented ultimately if a future industrial society were determined to do so.
1. The black hole generator
A SBH (Schwarzschild Black Hole in a quiescent steady state – a black hole that does not rotate ) could be artificially created by firing a huge number of gamma rays from a spherically converging laser. The idea is to pack so much energy into such a small space that a BH will form. An advantage of using photons is that, since they are bosons, there is no Pauli exclusion principle to worry about. Although a laserpowered black hole generator presents huge engineering challenges, the concept appears to be physically sound according to classical general relativity.
A nuclear laser can convert on the order of 10^−3 of its rest mass to radiation, we would need a lasing mass of order one billion tons to produce the pulse. This should correspond to a mass of order 10 billion tonnes for the whole structure (the size of a small asteroid). Such a structure would be assembled in space near the sun by an army of robots and built out of space-based materials.
2. The drive
For a SBH to drive a starship. We need to accomplish 3 things.
Design requirements for a BH starship
1. use the Hawking radiation to drive the vessel
2. drive the BH at the same acceleration
3. feed the BH to maintain its temperature
Item 3 is not absolutely necessary. We could manufacture a SBH, use it to drive a ship one way, and release the remnant at the destination. However this would limit us greatly as to performance, and be very disappointing in the powerplant application discussed below.
The most optimistic approach is to solve requirements 2 and 3 together by attaching particle beams to the body of the ship behind the BH and beaming in matter. This would both accelerate the SBH, since BHs “move when you push them” and add mass to the SBH, extending the lifetime.
3. The powerplant
This has already been proposed by Hawking. We simply surround the SBH with a spherical shield, and use it to drive heat engines. (Or possibly use gamma ray solar cells, if such things be.) This would have an enormous advantage over solar electric power in that the energy would be dense and hence cheaper to accumulate.
The 3 machines here really form a tool set. Without the drive, getting the powerplant near Earth where we need it would be very difficult. Without the generator, it would require the good fortune to find a primordial SBH to implement the proposal.
4. The self-driven generator
The industry formed by our first 3 machines would not yet be really mature. To fully tap the possibilities we would need a fourth machine, a generator coupled to a family of SBHs which could be used to charge its laser. Assuming we can feed a SBH as discussed above, we would then have a perpetual source of SBHs, which could run indefinitely on water or dust or whatever matter was most convenient.
A civilization equipped with our four machine tool set would be almost unimaginably energy rich. It could settle the galaxy at will.
What BHs are long-lived enough and powerful enough for interstellar
SBHs of radii less than 1 attometer are incredibly powerful. Note however that the life expectancy of a BH with a radius of 0.16 attometers is less than about 2 weeks. In order for such a BH to last significantly longer than that, an external agent must force-feed it mass-energy at a rate of many kilograms per second. As we have emphasized throughout the text, It is unknown whether SBHs, since they are so very small, can feed on anything at all, let alone many kilograms per second. If SBHs with radii on the order of 0.1 attometers could be force-fed at sufficiently high rates, by using a feeding system whose mass is small compared to the mass of the SBH, then it is not hard to believe that such SBHs could be very useful as power sources for starship propulsion systems – if their power can be harnessed efficiently. In the following however, we will assume that SBHs cannot be fed. Even in this “worst case scenario,” it turns out that SBHs could still turn out to be useful for interstellar travel.
We note that guiding a BH is less difficult than feeding it, because it is only necessary to scatter radiation off the BH to impart momentum to it. If even this is impossible, it is hard to see how to build any drive at all. About the fastest type of interstellar voyage that human beings could physically tolerate would be a one-way trip from Earth to Alpha Centauri (a distance of just over 4 light years) which accelerates at a proper acceleration of 1 g for the first half of the voyage and decelerates at 1 g for the second half. In this way, the travelers arrive at Alpha Centauri with zero relative speed. The trip would only take about 3.5 years from the perspective of the travelers (thanks to Special Relativity).
A BH with a life expectancy of about 3.5 years has a radius of about 0.9 attometers. Unless SBH lifetimes can be significantly extended via feeding, a manned interstellar vehicle powered by an on-board SBH requires SBHs of at least this initial size (and most likely quite larger). Conceivably, unfed SBHs of radii less than 0.9 attometers, having less than 3.5 year life expectancies, could be used to rapidly accelerate interstellar robotic probes to relativistic speeds. Robotic probes do not necessarily need to “stop” and could tolerate much larger accelerations than humans. The problem of navigating such objects could be difficult however.
The SBH would have to be ejected (or otherwise escaped from) before it explodes.
A SBH with a radius of 0.9 attometers has a mass of about 606,000 tonnes and a power output of about 160 petawatts. Over a period of only 20 days a 160 petawatt power source emits enough energy to accelerate 606,000 tonnes up to about 10% the speed of light. Of course, it is unrealistic to suppose that the emitted energy can be converted into kinetic energy with 100% efficiency, but even if the conversion occurs with an efficiency of only 10%, it only takes 10 times longer to deliver the requisite kinetic energy.