In pondering my post about the Great Silence, and hypothetical advanced civilizations planning on outliving the stars to take up residence around supermassive black holes, I looked to see if there was an online Hawking radiation calculator and, yup, there is:

Hawking Radiation Calculator

Easy to use; enter a value for any quantity, the other values are automatically generated. Some examples:

• If you start off with a 1 billion solar mass black hole, the expected lifetime will be 2.1X10^94 years. Long time. But the power emitted while that massive is a paltry 9X10^-47 watts, which might be a bit tricky to live on, even at a really slow rate.
• If your want one watt of power output, you need a black hole substantially smaller than Earth, 1.9X10^13 metric tons. The lifespan of such a black hole is a mere 1.8×10^25 years. However, this could be extended indefinitely. The lifespan calculation assumes that the black hole is left alone to progress naturally… nothing is added in. So as the black hole evaporates, it loses mass, gets smaller, gets hotter, spits out more power and, in the last second, goes out with a bang. But if you dump mass into the black hole at the same rate that energy comes out, the black hole will be extended indefinitely.

Now assume that your civilization wants to make it to 10^100 years at one watt. Seems a little low-power to me, but go with it. One watt ain’t a lot of power, but 10^100 years is a *looooong* time. One watt would require the conversion of 1.1126500560536E-17 kilograms per second, or about 3.9X10^90 kilograms total. That’s… a lot. That’s about 1.76X10^60 times the mass of the sun. If galaxies mass 100 billion suns, you’ll need about 1.76X10^49 entire galaxies to produce one watt for that long.

One could argue that that’s unrealistic.

However, if one could somehow gather that much mass together into one black hole (and I feel confident in stating “you can’t,” not least because the mass of the visible universe seems to be on the order of 25 billion galaxies), the expected lifetime of it would be 10^248 years. The diameter would be an impressive 10^48 *lightyears* and the power would be a trifling 2.9×10^-149 watts. This is of course much less than one watt. So how to get one watt out of it? Simple, slice a small 1.9X10^13 metric ton chunk out of the big black hole. How? Don’t ask me, but if you’ve got the ability to gather together a black hole that masses more than the universe, I’m sure you can figure it out. Now, you have a *tiny* black hole that radiates one watt, and one *gigantic* black hole that radiates approximately nothing. You’ll need to top off your small black hole every now and again to keep it’s mass relatively constant. How? Well, dip into the bigger hole. The big hole serves as long-term cold storage of mass, to be “burned” in the furnace of your small black hole.

Let’s say you’re a bit more constrained. You still need one watt, but you’re stuck with the mass of the galaxy, approximately 100 billion suns. If you can squish it all down into one cold-storage black hole of 100 billion suns and one small “furnace” black hole, one watt will burn through your supply of mass in only 5.67X10^50 years. That’s only 10^40 times the current age of the universe. If your processor is running at one-trillionth the speed of reality, that means you’ll only perceive a lifespan of 5.67X10^38 years. Hopefully you can get done whatever it is you were hoping to do in that time.

Other Fun Facts: so, your black hole has just about evaporated away. You enter “one second” into the “lifetime” box. With one second left to live, the black hole is only 3.4×10-20 centimeters in radius, but it’s putting out a toasty 6.8×10^21 watts, and has a mass of 228270.5 kilograms. Every last one of those kilograms will be converted to energy in that last second. if you’ve made the mistake of transporting your itty-bitty black hole to Earth, you’re going to make a heck of a dent with the resulting 4.9 million megaton blast.

Another example: let’s say you have a heavy particle collider, working with such power and speeds that you think it’s just possible that you will smack protons together hard enough to squish ’em into tiny little black holes. “Oh, no!” screech the protestors. “You’ll kill us all with your constant playing of god!”

Well… no. Let’s be astoundingly generous and say you can create a black hole massing one microgram, many orders of magnitude greater than the mass of a proton. The microgram-black hole will be at a temperature of 10^32 degrees. This is important, since the radiant energy at those power levels will produce *substantial” photon pressure at atomic scale dimensions. In essence, the black hole will have its own deflector shield, preventing other particles from being sucked in. What’s even better: the lifetime of the microgram black hole is only 8.4X10-44 seconds… and Planck time – the smallest unit of time that seems to exist, is about 10^43 seconds. This means that the black hole will cease to be a black hole in less time than it takes to do literally *anything.*

Ain’t science a hoot?