= Stefan-Boltzmann estimate of Schwarzschild evaporation time
{c}
{title2=$t_{\mathrm{evap}}=5120\pi G^2M_0^3/(\hbar c^4)$}
Approximate an isolated <Schwarzschild black hole> as emitting photon <blackbody radiation> from an area $16\pi G^2M^2/c^4$ at <Hawking temperature> $\hbar c^3/(8\pi Gk_BM)$. The <Stefan–Boltzmann law> gives $P=\hbar c^6/(15360\pi G^2M^2)$. Integrating $c^2dM/dt=-P$ gives the displayed lifetime, about $2\times10^{67}$ years for a solar mass. <Greybody factors> and additional emitted species modify the coefficient; the robust large-mass scaling is $M_0^3$, and the semiclassical calculation does not determine the final quantum-gravity endpoint.
// Target: general-relativity.bigb
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