Area bound on equal-mass Schwarzschild merger radiation ($E_{\mathrm{rad}}\le (2-\sqrt{2})m{c}^2$)

Two initially well-separated Schwarzschild black holes of mass $m$ each have total horizon area $32\pi G^2{m}^2/c^4$. If they merge into a Schwarzschild black hole, Hawking's area theorem gives final mass $M\ge \sqrt{2}m$. Conserved total energy then bounds escaped radiation by the displayed expression, or $1-1/\sqrt{2}$ of the initial rest energy. This is an upper bound under classical horizon and energy assumptions, not a proof that an actual merger can saturate it.