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

By C. Armendariz-Picon. 2002

148 citations recorded by the source corpus.

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, nonsingular, 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 nonzero mass solutions and conclude that at least a nonzero measure set of these solutions is stable.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2c648b8bb41ce120bd5527f4fee5107cf084e041

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Citations in the corpus

Instability of wormholes supported by a ghost scalar field: I. Linear stability analysis (2008, background): “We do so by first generalizing the master equation obtained in [9] to massive wormholes.”
Exotic solutions in General Relativity: Traversable wormholes and 'warp drive' spacetimes (2007, background): “For the Ellis’ drainhole [45, 46], Armendáriz-Picón [104] finds that it is stable against linear perturbations, whereas Shinkai and Hayward [105] find this same class unstable to nonlinear perturbations.”
Morris-Thorne wormholes with a cosmological constant (2003, background): “…Friedmann-Robertson-Walker universe with Minkowski spacetime or joining two Friedmann-Robertson-Walker universes [26] could be interpreted, after further matchings, as a wormhole joining a collapsing (or expanding) star to Minkowski spacetime or a wormhole joining two dynamical stars, respectively.”
Haloes of k-essence (2005, background): “(2) Following [5], we call such a scalar field a “k-field”.”
Phantom energy traversable wormholes (2005, background): “In fact, one can trace back to the 1970s examples of wormholes with a negative kinetic energy scalar [46, 47, 48, 49], which may be considered as the current phantom energy source [50].”
Stability of phantom wormholes (2005, unknown): “[25], in a rather different context).”