Would the Hawking radiation from a small black hole make a feasible propulsion source?

Question

I was wondering if a small black hole would make a feasible/possible propulsion source, and if so, how.

• Pros
  • Black holes release Hawking radiation, would should be easy to direct in a certain direction.
  • Literally anything, from garbage to planets could be fed into the black hole.
  • It could provide artificial gravity
  • You can charge black holes, making it easier to contain.
• Cons
  • The black hole could destroy the ship and everyone in it, and then it wouldn't being propelling anything

What size black hole would be possible, if any? At what rate should you feed it? How do you contain it safely?

We can assume basically any level of technological development that isn't magic (no gravity wizards). They also have near infinite amounts of energy.

Answer 1

Very interesting idea. Let me start with some relevant facts, as brought up in the comments.

A bh emits more radiation, becoming hotter as it becomes smaller. The temperature is inversely proportional to the black hole’s mass. But, the quantity of energy for a given temperature is reduced because the surface area gets smaller. Radius is ∝ mass, and surface area ∝ radius squared. So T is inverse to r². The size shrinks faster than temperature rises! But, black body radiation energy increases faster than temperature, so which wins?

In fact, (nicely posted on Wikipedia) $$\mathrm{Power} = \frac{\hbar c^6}{15360 \pi G^2 M^2}$$ Notice the mass squared in the denominator!

To calibrate the Power measurement, consider that a solar mass black hole emits $9 \times 10^{-29}$ watts. 1-second-lived black hole has a mass of $2.28 × 10^5$ kg has an initial power of $6.84 × 10^{21}$ W.

So, feeding a bh on mass you have on hand to keep it a constant size, and directing the radiation out the back, can deliver a required amount of power by sizing the bh appropriately.

How much power do you need? Use the formula and follow the example from wikipedia to find out. Now, look at the size of that bh. Hmm, turning down the power means carting around even more mass.

The problem is that the radius of the bh is 1000 times smaller than a proton!

How can you feed it the large amount of mass needed to retain equilibrium? I think it can’t be done, even neglecting that the output will blow everything away from it. You can’t get enough mass in a small enough volume to be swallowed at that rate, without it being another black hole.

Now nevermind that it can’t be done as implied. Maybe it’s a large habitat undergoing very low acceleration, like today’s ion drives. How do you keep it tethered? A bh can be charged electricly, but it tries to shed its charge first thing, as the radiation will be charged.

So, feed it highly charged matter to keep it charged, and rely on the charged radiation to direct it, and the charge on the bh to keep it centered in the cavity. Throw the leftover opposite charged matter in the exhaust after it is directed.

A more practical way to get power from a bh is via the ergosphere. However, that would be done with a non-microscopic (not hot) bh.

Answer 2

JDługosz answered this great, with numbers and everything. And the question has been considered by at least two scientists, namely Crane & Westmooreland - their paper can be found in arxiv here.

Containing the black hole:

When it comes to containing it safely, well, I the authors of the aforementioned paper concluded that a BH confine itself. All that has to be done is to avoid colliding with it. I would say it is a pretty disengaged way of addressing the issue, but then again, maybe it was a no-brainer and I am the only reader left wishing for a more in-depth explanation of this facet of the problem.

Feeding the black hole:

They need not be fed at all to be efficient. If that was the case, they would likely be unfeasible as propulsion methods (it is quite likely that they are unfeasible anyway, but for other reasons than the feeding issue). Feeding a black hole with a radius of 0.9 attometers (10 to the power of minus 18) with iron, would be hard for the reason that most likely the BH would zip right through the iron bar. The average distance between bonded iron atoms is 0.7 picometer (10 to the power of minus 12), meaning we could fit a million BHs in the distance between two iron atoms in a piece of solid iron. The feeding procedure would take the term micro managing to a whole new level.

Size(s) of the black hole(s):

Which size(s) of the black hole(s) would be possible? According to Crane & Westmoreland, there is a sweet spot - and that is a BH large enough to exist and be able to accelerate/decelerate the ship during the entire voyage. Yet not larger than necessary, since BH give off Hawking radiation in an inverse proportion to their size, as mentioned by JDługosz. A bigger hole will give you less energy output. The radius of 0.9 attometers I used as an example was not a random number, but a radius that would mean that the BH would exist during 3.5 years. That is the relativistic time that a one-way trip from Earth to Alpha Centauri (~4 ly away) would take, i.e. that would be the length of the journey as measured by the clocks on board the ship, if said ship were to accelerate at 1 g for half the trip, and then decelerate at 1 g during the other half (I must presume they have assumed some value for the mass of the ship to be able to calculate this, but I couldn't find it anywhere in the text).

Smaller BHs would be useful for fast accelerations of probes or missiles. Larger BHs would be useful for longer trips. So yes, there are "sweet spots" when it comes to the size of a BH when used for propulsion. These sizes depend upon the length of the journey, the mass of the ship, etc.

But too large BHs, and the time needed to generate enough energy to accelerate the mass of the BH itself would be very long. Please see the table and the examples explained in the article for more information.

Conclusion:

Given the size of the proposed BHs, we could most likely not ignore quantum effects. And given their density, we could not ignore the gravity effects either. Since we currently lack understanding of gravity at the quantum level, and since our understanding of black holes from both a theoretical and experimental standpoint is extremely poor, I would say that it is not possible to determine the feasibility of this propulsion method at this stage of our technological development. The question would best be readdressed when we have a workable quantum theory of gravity, if it is to remain within the realm of hard science, rather than a the field of science fiction.

EDIT: Just found a newer paper by Crane on the subject here a minute ago. Haven't read it though, but it might be relevant.

Answer 3

There's a paper

http://arxiv.org/pdf/0908.1803.pdf

By these 2 guys

https://www.phys.ksu.edu/personal/westmore/

http://www.math.ksu.edu/people/personnel_detail?person_id=1330

To summarize: Yes it is likely possible but you need to point particle beams at the black hole both to keep its size stable and to control its position.

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.

We shall discuss these three problems in outline only here; at the level of engineering they will each require an extended discussion. It is not hard to see how we might satisfy requirement 1. We simply position the SBH at the focus of a parabolic reflector attached to the body of the ship. Since the SBH will radiate gamma rays and a mix of particles and antiparticles, this is not simple. The proposal has been made in the context of antimatter rockets, to make a gamma ray reflector out of an electron gas [11].

It is not clear if this is feasible (e.g., [2]).

Alternatively, we could allow the gamma rays to escape and direct only the charged particle part of the Hawking radiation (cf. [2]), although this produces a less capable ship. To improve the performance, we could add a thick layer of matter which would absorb the gamma rays, reradiate in optical frequencies, and focus the resulting light rays. An absorber which stops only gamma rays heading towards the front of the ship and allows the rest to escape out the back causes gamma rays to radiate from the ship asymmetrically. In this way, even the escaping non-absorbed gamma rays contribute some thrust (cf. [12] or [13]). Modulo safety concerns, one would not want the absorber to be too massive. An extremely massive absorber could burden the mass of vehicle so much that the extra thrust it helps to deliver does not lead to an improved acceleration.

Yet another idea for the utilization of gamma ray energy is to exploit pair production phenomena. By interacting with the electric field of atomic nuclei, high energy gamma rays can be converted into charged particle-antiparticle pairs such as electrons and positrons. These particles can be directed by electromagnetic fields. It is not likely that even half of the gamma ray energy can be utilized in this manner however (see Vulpetti [14], [15]).

It might be advantageous to use the Hawking radiation to energize a secondary working substance which can then be ejected as exhaust (as is done in thermal and ion rockets). However, the working substance must be ejected at 10 relativistic speeds so that the specific impulse will be high enough for interstellar travel.

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”(see [3] p270), and add mass to the SBH, extending the lifetime.

The delicate thing here is the absorption cross section for a particle going into a BH. We intend to investigate this question in the future. If simply aiming the beam at the SBH doesn’t work, we can try forming an accretion disk near the SBH and rely on particles to tunnel into it. Alternatively, we could use a small cluster of SBHs instead of just one to create a larger effective target, charge the SBH etc. It is also possible that because of quantum effects SBHs have larger than classical radii, due to the analog of zero point energy. This point must remain as a challenge for the future.

Answer 4

AS noted, a black hole has a pretty impressive power output, especially micro black holes.

The downside is ones with the practical mass to power a ship or colony are also the mass of asteroids to small moons. Outside of the practical engineering difficulties of feeding mass to an object as small as an atomic nucleus, it also means your ship is hauling around the mass of the black hole. Much like ion drives, the gain in performance using the engine is offset by the extra mass you need to carry around (in the case of an ion drive, you either need a nuclear reactor and shielding, or hectares of solar panels to provide the energy for a large ion or plasma drive).

A full discussion is in this paper: ARE BLACK HOLE STARSHIPS POSSIBLE? By Louis Crane and Shawn Westmoreland, Kansas State University.