## Archive for January, 2011

### Now If I Can Just Find a Fez

Today I decided to buy a toy replica of the 11th Doctor’s sonic screwdriver and was amused at what else it suggested I buy:

Then again…bow ties are cool.

### Black Hole Power Generator Equations

For those interested here are the equations for the black hole generator. The three main pieces of information we are interested is the black hole’s mass M (in kilograms), the power output P (in Watts), and the time it will take to evaporate (basically, the safety margin) T (in seconds). If you know one, it is possible to obtain the other two:

P = 3.563 x 10^32 / M^2 = 6.838 x 10^21 / T ^ (2/3)

T = 8.407 x 10^-17 * M^3 = 5.654 x 10^32  /  P ^ (3/2)

M = 2.283 x 10^5 * T ^ (1/3) = 1.888 x 10^16 / P ^ (1/2)

Rechecking the numbers it appears I actually made errors in calculating the black hole’s parameters in the previous post, so I went back and corrected them.

### Black Hole Power Generator

For the past few days I’ve been kicking around the idea of using a black hole as a power generator. It seems counter-intuitive: a black hole absorbs all matter, right? How would one use it to create power? The answer lies in the fact that all black holes emit what is called Hawking Radiation.

In 1974, Steven Hawking showed that black holes have temperature due to quantum effects, and anything with a temperature above absolute zero will create black-body radiation. This radiation obviously has energy, which comes from the mass of the black hole itself (the details aren’t particularly important, only the big picture). Essentially, black holes will slowly evaporate and thus shrink. Even stranger, as they get smaller, black holes will emit more and more radiation until they have no more mass left and completely disappear.

So, what if we were to construct a black hole and harness this energy as it is emitted? We capture it (more on this in a bit), build, say, power cells around it, use it as a power plant? Now obviously, it would be bad to let the black hole evaporate completely as the power output increases enormously as it shrinks. In a practical sense, the black hole “goes critical” and explodes. So…what if we continually feed it with matter to keep it at a relatively “tame” level? Say we have our black hole, and we’ve tuned it to produce, say, 10 TeraWatts of power, enough to power the Earth. It’s mass would be (if my math skillz haven’t failed me) about 1.9 million 6 million tons and be about one ten-millionth of a billionth two millionths of a billionth (2 x 10^-15) of a centimeter in diameter. 10 TeraWatts means it will lose roughly 0.11 gram per second in radiation and every year it will lose about 3500 kg in mass. If we continually input matter at that same rate, the black hole will remain stable and continually output 10 TeraWatts.

The reason this is so intriguing is because the conversion rate is (theoretically) 100% efficient. We put a kilogram of matter into the black hole, we’ll get (eventually) a kilogram of mass-energy back out, and the black hole will be exactly the same as when we began. Compare this to fusion where the efficiency is only around 0.7%. That’s a huge difference! Even better, any matter at all will work, not just hydrogen and helium. Elements that are past iron on the periodic table are useless for fusion, but work just fine with black hole generator.

Creating such a black hole is left as an exercise to the reader, but here’s how you hold it. Well you actually don’t have to “hold” it. If you’re building this power generator in space, you can just let the black hole freely orbit the Sun or the Earth and construct your power collectors around it, but it wouldn’t be very mobile. If you actually wanted to take it with you, you could initially feed the black hole with some amount of electrically-charged matter. If a black hole swallows an electron, the black hole itself will then have a negative charge. You can use this fact to electrostatically levitate the black hole, like how if you stack two magnets on a stick with the same poles pointing towards each other, one will stay hovering above the other in mid-air.  Neat huh? One just needs to continually input charged particles to keep the charge on it.

Even the threat of the black hole “going critical” is literally very remote. If left to physics alone our hypothetical 6-million-ton black hole won’t actually explode for over 18,000 568,000 years.

Anyway, looking around the web, it seems as though someone has already written a paper on this. I suppose I’ll take it as a good sign that my own musings are paper-worthy material (though in their paper they use the black hole to power a space ship), just the rigor is lacking.