Quantum gravity on the black hole horizon

TL;DR

This paper investigates quantum gravitational effects at the black hole horizon by summing virtual graviton exchanges non-perturbatively, supporting the scattering matrix approach to quantum black holes in a semi-classical regime.

Contribution

It introduces a non-perturbative summation of virtual gravitons at the black hole horizon, extending previous gravitational backreaction studies and generalizing eikonal calculations to semi-classical black holes.

Findings

Summation of virtual graviton exchanges is possible non-perturbatively.

The relevant collision energies can be much higher than Planckian for semi-classical black holes.

Supports the scattering matrix approach as a viable framework for quantum black hole analysis.

Abstract

We study scattering on the black hole horizon in a partial wave basis, with an impact parameter of the order of the Schwarzschild radius or less. This resembles the strong gravity regime where quantum gravitational effects appear. The scattering is governed by an infinite number of virtual gravitons exchanged on the horizon. Remarkably, they can all be summed non-perturbatively in $\hbar$ and $\gamma \sim M_{Pl}/M_{BH}$. These results generalise those obtained from studying gravitational backreaction. Unlike in the eikonal calculations in flat space, the relevant centre of mass energy of the collisions is not necessarily Planckian; instead it is easily satisfied, $s \gg \gamma^2 M^2_{Pl}$, for semi-classical black holes. The calculation lends further support to the scattering matrix approach to quantum black holes, and is a second-quantised generalisation of the same.