The Virtual Black Hole in 2d Quantum Gravity and its Relevance for the S-matrix

TL;DR

This paper demonstrates that 2d quantum gravity theories can be treated perturbatively, revealing a virtual black hole in scalar scattering and resulting in a finite S-matrix for gravitational s-wave interactions.

Contribution

It shows the classical black hole formation mechanism appears at tree level and introduces a finite S-matrix for scalar scattering in 2d quantum gravity with non-minimal coupling.

Findings

Identification of a virtual black hole in scalar scattering.

Finite S-matrix for non-minimally coupled scalars.

Tree-level black hole formation mechanism confirmed.

Abstract

As shown recently 2d quantum gravity theories -- including spherically reduced Einstein-gravity -- after an exact path integral of its geometric part can be treated perturbatively in the loops of (scalar) matter. Obviously the classical mechanism of black hole formation should be contained in the tree approximation of the theory. This is shown to be the case for the scattering of two scalars through an intermediate state which by its effective black hole mass is identified as a "virtual black hole". We discuss the lowest order tree vertex for minimally and non-minimally coupled scalars and find a non-trivial finite S-matrix for gravitational s-wave scattering in the latter case.