Black Hole Mass and Energy Requirements for Sustainable Hawking Radiation

[tomwinwa]

This question pertains to a Sci-Fi story I am writing, using the concept of a black hole and Hawking radiation which is developed as an energy source, and I'd like to get some technical details worked out.

My understanding is that an extremely small black hole will very quickly cease to exist due to Hawking radiation, releasing energy in the process. What amount of matter would be required in such a black hole to release the energy equivalent to a fusion bomb? And what would be the best material to use to create such a black hole?

Assume for the sake of this question that a method has been developed to simultaneously place all the requisite mass in a single point. This would be enormously helpful to know to my story.

Thanks!

 

[mfb]

Here is a calculator.

1 MT TNT equivalent correspond to a mass of 47 gram, scale as you want. The largest nuclear weapon ever detonated had a yield of 50 MT, or the mass equivalent of about 2.4 kg.
Some fraction of the mass is emitted as neutrinos that don't contribute to the yield, if in doubt round the values up not down.

The calculator underestimates the radiation for black holes that small, but it doesn't matter for a weapon application at this yield: It is basically instantaneous anyway.

What amount of matter would be required in such a black hole to release the energy equivalent to a fusion bomb? And what would be the best material to use to create such a black hole?

There is no known way to convert matter into a black hole unless you have a few times the mass of the Sun available. It might be possible to produce gamma ray lasers and make the beams collide to form a black hole, but (a) that is speculative and (b) if you have these lasers you can directly use them as weapon, there is no point in an intermediate black hole. Unless you produce a black hole massive enough to store it, then it could be interesting as well. Such a black hole, thrown into a planet, would destroy the planet over time...

 

[tomwinwa]

50 MT (plus or minus) is more than sufficient for what I have in mind in my novel, and 2.4 kg is about in line with what I suspected.

I presume any material would serve as long as it is the correct mass, so in this case I'm thinking to use lead.

As for the mechanism, that's the one SciFi hand-waveium "gimme" I'm going to take, but what I have in mind is a completely different method which I think will nevertheless be credible once I explain it, and was inspired by the creative applications being found for...ummm, I think you'll have to wait for the book. :-)

 

[mfb]

1.2 kg of matter and 1.2 kg of antimatter would do the same job without needing so much handwaving. Well, again some energy would be lost to neutrinos, so maybe 1.5 kg each.

 

[tomwinwa]

But it's a really *interesting* handwave, and the containment of the antimatter would require more handwaving than the solution I have in mind. I'm still writing the rough draft but if you want to read the alpha draft I'll send it to you...it's a SF noir mystery, with the tone of Blade Runner.