Probing the chronology protection conjecture via scalar quasiresonance

Abstract

Hawking’s Chronology Protection Conjecture (CPC) proposes that the laws of physics prevent the formation of time machine. In his original argument, fields near a would-be chronology horizon undergo repeated blueshifts, signaling the onset of instabilities. In this work, we obtain an exact analytical solution of the Klein–Gordon equation for a relativistic scalar field in a spherically symmetric Morris–Thorne traversable wormhole. By polynomializing the radial equation and analyzing the Klein–Gordon current, we find that the resulting radiation modes generically possess complex eigenfrequencies: unstable modes grow in time and propagate inward toward the throat, while stable modes decay and flow outward. This directional instability prevents stationary configuration required to support time machine constructions, providing a dynamical obstruction consistent with Hawking’s Chronology Protection Conjecture.