Conformally Invariant Boundary Conditions for Dilaton Gravity

TL;DR

This paper explores quantum boundary conditions in two-dimensional dilaton gravity, revealing how different incident matter pulses lead to boundary oscillations or black hole formation, characterized by nonlinear differential equations.

Contribution

It introduces conformally invariant boundary conditions for dilaton gravity and analyzes their effects on matter scattering and black hole formation.

Findings

Weak pulses cause damped boundary oscillations

Large pulses lead to black hole creation

Boundary response governed by nonlinear differential equations

Abstract

Quantum mechanical boundary conditions along a timelike line, corresponding to the origin in radial coordinates, in two-dimensional dilaton gravity coupled to $N$ matter fields, are considered. Conformal invariance and vacuum stability severely constrain the possibilities. The simplest choice found corresponds to a nonlinear Liouville-type boundary interaction. The scattering of low-energy matter off the boundary can be computed perturbatively. It is found that weak incident pulses induce damped oscillations at the boundary while large incident pulses produce black holes. The response of the boundary to such pulses is semi-classically characterized by a second order, nonlinear ordinary differential equation which is analyzed numerically.