Reference: Moore, Thomas A., A General Relativity Workbook, University Science Books (2013) – Chapter 16; Problem P16.2.
We’ve seen that through radiation, a black hole can eventually evaporate in a time :
where is the solar mass. Clearly if we’re going to observe black hole evaporation, its mass must be considerably less than the sun’s. Suppose black holes were formed during the big bang at years ago. If the black hole is just evaporating now, its mass would have been:
To put this in perspective, this is equivalent to an asteroid, with a typical rocky density of , with a radius of
To see how much energy is released in the final second of the black hole’s life, we can start with the equation we had earlier from the Stefan-Boltzmann relation:
If we integrate this from to a time one second before the present, at which time the black hole’s remaining mass is , then
However, is just , where is the present time, so that . Therefore the mass remaining 1 second before complete evaporation is:
In GR units, a time of 1 second is so we get for the mass
This is equivalent to
which is about 100 times the energy released in an atomic bomb blast.