Here's the derivation of the relationship between time and mass for a black hole radiating and absorbing as a blackbody. It expresses time as a function of mass. The strategy used here in deriving this relationship is this:

- Find an expression for the rate mass loss of a black hole due to Hawking radiation.
- Find an expression for the rate mass gain of a black hole due to cosmic background radiation.
- Equate the two expressions found; rate in equals rate out at equilibrium.

Since we have graphs and derivations to back us up, don't bother sending in criticisms to Kevin or John. Ha ha, just kidding!

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