Traversable Wormholes and Classical Scalar Fields

Abstract

I prove that general relativity admits no asymptotically well-behaved static spherically symmetric traversable wormholes supported by classical scalar fields and nonexotic matter. The theorem holds for all values of the scalar field curvature coupling parameter $\xi$, even though fields with $\xi >0$ are capable of violating the average null energy condition. Good asymptotic behaviour (the effective Newton's constant being positive and finite at both ends of the wormhole) can only be achieved by introducing additional exotic matter, which must itself violate the null energy condition over some region of nonzero volume. These results are insensitive to the number of scalar fields, the form of their potentials, and the coupling between the fields and the additional matter.

6 pages; published version

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Cited by in corpus (9)

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• Wormholes in conformal gravity
• Wormhole geometries in fourth-order conformal Weyl gravity
• Rotating traversable wormhole geometries in the presence of three-form fields
• Traversable Wormholes induced by Stress Energy Conservation: combining Casimir Energy with a scalar field
• Averaged null energy condition and quantum inequalities in curved spacetime
• Stability of spherical thin-shell wormholes in scalar-tensor theories