Soft graviton exchange and the information paradox

Understand

We show that there is a remarkable phase in quantum gravity where gravitational scattering amplitudes mediated by virtual gravitons can be calculated explicitly in effective field theory, when the impact parameter $b$ satisfies $L_{Pl}\ll b \lesssim R_S$, with $R_S$ being the Schwarzschild radius.

• This phase captures collisions with energies satisfying $\sqrt{s}\gg \gamma M_{Pl}$ (with $\gamma \sim M_{Pl}/M_{BH}$) near the horizon.
• We call this the black hole eikonal phase, in contrast to its flat space analogue where collisions are trans-Planckian.
• Hawking's geometric optics approximation neglects gravitational interactions near the horizon, and results in thermal occupation numbers in the Bogoliubov coefficients.