= Area bound on equal-mass Schwarzschild merger radiation
{title2=$E_{\rm rad}\le(2-\sqrt2)mc^2$}
Two initially well-separated <Schwarzschild black holes> of mass $m$ each have total horizon area $32\pi G^2m^2/c^4$. If they merge into a <Schwarzschild black hole>, <Hawking's area theorem> gives final mass $M\ge\sqrt2m$. Conserved total energy then bounds escaped radiation by the displayed expression, or $1-1/\sqrt2$ 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.
Back to article page
