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

Understand

In the spirit of studying the information paradox as a scattering problem, we pose and answer the following questions: i) What is the scattering amplitude for $N$ particles to emerge from a large black hole when two energetic particles are thrown into it? ii) How long would we have to wait to recover the information sent in? The answer to the second question has long been expected to be Page time, a quantity associated with the lifetime of the black hole.

• We answer the first by evaluating an infinite number of `ladder of ladders' Feynman diagrams to all orders in $M_{Pl}/M_{BH}$.
• Such processes can generically be calculated in effective field theory in the black hole eikonal phase where scattering energies satisfy $E M_{BH} \gg M^{2}_{Pl}$.
• Importantly, interactions are mediated by a fluctuating metric; a fixed geometry is insufficient to capture these effects.