Semi-classical wormholes and time machines are unstable

TL;DR

The paper demonstrates that semi-classical Lorentzian wormholes and time machines are inherently unstable because their violation of the null energy condition leads to perturbative instability, due to the quantum state localization in phase space.

Contribution

It establishes a fundamental instability of semi-classical wormholes and time machines arising from their violation of the null energy condition and quantum state localization.

Findings

Semi-classical wormholes violate the null energy condition.

Such configurations are unstable to small perturbations.

Quantum state localization implies classical evolution, leading to instability.

Abstract

We show that Lorentzian (traversable) wormholes and time machines with semi-classical spacetimes are unstable due to their violation of the null energy condition (NEC). Semi-classicality of the energy-momentum tensor in a given quantum state (required for semi-classicality of the spacetime) implies localization of its wavefunction in phase space, leading to evolution according to the classical equations of motion. Previous results related to violation of the NEC then require that the configuration is unstable to small perturbations.