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

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

2002-01-08

arxiv.org/abs/gr-qc/0201027v2

Phys.Rev. D65 (2002) 104010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, 4 figures, uses RevTeX4. v2: Changes to accommodate added references. Statement about masses of the wormhole correct

Scientific paper

10.1103/PhysRevD.65.104010

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.

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