= Semiclassical cubic mass law for Schwarzschild evaporation
{title2=$M(t)^3=M_0^3-3\alpha t$}
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.
Back to article page
