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In the spirit of studying the information paradox as a scattering problem, wepose and answer the following questions: i) What is the scattering amplitudefor $N$ particles to emerge from a large black hole when two energeticparticles are thrown into it? ii) How long would we have to wait to recover theinformation sent in? The answer to the second question has long been expectedto be Page time, a quantity associated with the lifetime of the black hole. Weanswer the first by evaluating an infinite number of `ladder of ladders'Feynman diagrams to all orders in $M_{Pl}/M_{BH}$. Such processes cangenerically be calculated in effective field theory in the black hole eikonalphase where scattering energies satisfy $E M_{BH} \gg M^{2}_{Pl}$. Importantly,interactions are mediated by a fluctuating metric; a fixed geometry isinsufficient to capture these effects. We find that the characteristic timespent by the particles in the scattering region (the so-called Eisenbud-Wignertime delay) is indeed Page time, confirming the long-standing expectation. Thisimplies that the entropy of radiation continues to increase, after theparticles are thrown in, until after Page time, when information begins tore-emerge.

$2 \rightarrow 2N$ scattering: Eikonalisation and the Page curve