On a class of stable, traversable Lorentzian wormholes in classical general relativity

TL;DR

This paper explores the conditions under which stable, traversable Lorentzian wormholes can exist in classical general relativity, identifying specific scalar field models that support such geometries and analyzing their stability.

Contribution

It introduces a restrictive class of scalar field Lagrangians capable of supporting traversable wormholes and proves the stability of certain solutions within this class.

Findings

Stable, zero-mass wormholes are analytically demonstrated.

A non-zero measure set of solutions are shown to be stable.

Simple models with reversed sign kinetic terms can produce traversable wormholes.

Abstract

It is known that Lorentzian wormholes must be threaded by matter that violates the null energy condition. We phenomenologically characterize such exotic matter by a general class of microscopic scalar field Lagrangians and formulate the necessary conditions that the existence of Lorentzian wormholes imposes on them. Under rather general assumptions, these conditions turn out to be strongly restrictive. The most simple Lagrangian that satisfies all of them describes a minimally coupled massless scalar field with a reversed sign kinetic term. Exact, non-singular, spherically symmetric solutions of Einstein's equations sourced by such a field indeed describe traversable wormhole geometries. These wormholes are characterized by two parameters: their mass and charge. Among them, the zero mass ones are particularly simple, allowing us to analytically prove their stability under arbitrary space-time dependent perturbations. We extend our arguments to non-zero mass solutions and conclude that at least a non-zero measure set of these solutions is stable.