Chronology Protection in Two-Dimensional Dilaton Gravity

TL;DR

This paper investigates the global structure of a 1+1 dimensional dilaton gravity universe, analyzing classical and quantum spacetimes with closed timelike curves, and discusses their stability and conditions for their reappearance.

Contribution

It provides a classical solution with closed timelike curves and examines quantum effects that prevent their reemergence without fine-tuning.

Findings

Classical solutions with closed timelike curves are unstable due to matter

Quantum effects suppress the reappearance of closed timelike curves unless parameters are fine-tuned

The study enhances understanding of chronology protection in two-dimensional dilaton gravity

Abstract

The global structure of 1 + 1 dimensional compact Universe is studied in two-dimensional model of dilaton gravity. First we give a classical solution corresponding to the spacetime in which a closed time-like curve appears, and show the instability of this spacetime due to the existence of matters. We also observe quantum version of such a spacetime having closed timelike curves never reappear unless the parameters are fine-tuned.