The virtual black hole in 2d quantum gravity

TL;DR

This paper investigates the formation of virtual black holes in 2D quantum gravity, showing that classical black hole mechanisms appear in the tree approximation and analyzing scalar scattering with and without mass.

Contribution

It demonstrates the presence of virtual black holes in 2D quantum gravity and explores scalar scattering amplitudes, including the effects of scalar mass and boundary conditions.

Findings

Tree approximation contains classical black hole formation.

Massless scalar scattering amplitude diverges without boundary conditions.

Massive scalar scattering yields finite S-matrix elements.

Abstract

As shown recently (W. Kummer, H. Liebl, D.V. Vassilevich, Nucl. Phys. B 544, 403 (1999)) 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''. The present discussion is restricted to minimally coupled scalars without and with mass. In the first case the probability amplitude diverges, except the black hole is ``plugged'' by a suitable boundary condition. For massive scalars a finite S-matrix element is obtained.