Soft graviton exchange and the information paradox

Abstract

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 LPl≪b≲RS, with RS being the Schwarzschild radius. This phase captures collisions with energies satisfying s≫γMPl (with γ∼MPl/MBH) near the horizon. We call this the black hole eikonal phase, in contrast to its flat space analog 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. We show that these interactions are mediated by graviton exchange in 2→2 scattering near the horizon, and explicitly calculate the S-matrix nonperturbatively in MPl/MBH. This involves a resummation of infinitely many ladder diagrams near the horizon, all mediated by virtual soft gravitons. The S-matrix turns out to be a pure phase upon this resummation and is agnostic of Planckian physics and any specific ultraviolet completion. In contrast to the flat-space eikonal limit, the black hole eikonal phase captures collisions of extremely low energy near the horizon.