Quantum backreaction and stability of topological wormholes

TL;DR

This paper analyzes the quantum stability of a specific topological wormhole by calculating quantum backreaction effects, showing that quantum corrections can either stabilize or destabilize the wormhole depending on counterterms, and that traversability can be maintained.

Contribution

It provides a detailed calculation of quantum backreaction on a topological wormhole and explores how quantum effects influence its stability and traversability.

Findings

Quantum effects can induce either stabilization or destabilization.

A classically traversable wormhole remains traversable under quantum backreaction.

The stability depends on the choice of finite counterterms.

Abstract

We investigate the quantum stability of a timelike topological wormhole with a simple geometry $M_2 \times S^2$, supported classically by anisotropic fluid. We compute the one-loop quantum backreaction generated by the vacuum fluctuations of a minimally coupled, massive scalar field propagating on the wormhole background. Using dimensional regularization we renormalize the one-loop energy-momentum tensor and identify the necessary gravitational counterterms. We then solve the semiclassical Einstein equations to linear order in $\hbar$ for both time-dependent and static metric {\it Ans\"{a}tze}. Depending on the choice of finite counterterms, the quantum effects can induce either negative or positive angular pressure, which will tend to destabilize or stablize the wormhole, respectively. We also show that a classically traversable wormhole will remain traversable when the quantum backreaction is taken into account. It would be of interest to investigate whether these conclusions remain true when the equations of semiclassical gravity are self-consistently solved.