 Semiclassical cubic mass law for Schwarzschild evaporation

For a large isolated Schwarzschild black hole with a fixed effective set of radiated species, Hawking radiation has $T\propto M^{-1}$ and luminosity $P=\alpha /M^2$ in natural units. Integrating $dM/dt=-\alpha /M^2$ gives the displayed law. A horizon-area blackbody radiation estimate gives $\alpha =1/(15360\pi )$; greybody factors and species change it. With mass-dependent $\alpha$, integrate $t={\int }_{M(t)}^{M_0}{m}^{2}dm/\alpha (m)$ instead. The semiclassical gravity approximation fails near Planck mass, so a formal zero of the cubic law does not settle the final state.