Calculating the Time to Evaporate of Small Black Holes
Earlier today, Uncle Bob Martin twittered “Micron sized black hole will evaporate in 200 billion years and has the mass of a cubic kilometer of water.”
Curious about the calculation, I looked up the formula in Wikipedia’s article on Hawking radiation:
Next, to fill in the variables.
Gravitational constant is: 6.67428e-11 m3 kg-1 s-2
Dirac’s constant is: 1.054571e-34 m2 kg s-1
Speed of light is: 2.99792458e+8 m s-1
Black hole mass (1 cubic kilometer of water) is: 1e+12 kg.
Calculating in my trusty irb:
irb(main):001:0> tev = (5120 * Math::PI * 6.67428e-11**2 * 1e+12**3) / (1.054571e-34 * 2.99792458e+8**4)
=> 8.41143401030793e+19
irb(main):002:0> tev_in_years = tev / (60*60*24*365)
=> 2667248227520.27
2.66725 trillion years.
Note 1: I had tweeted earlier that it would take 1e+49 years, because I had screwed up the cubing of the mass of the black hole.
Note 2: This black hole would radiate at about 356 megawatts, a little less than an average US nuclear power plant.
