Traversable Wormholes and Classical Scalar Fields

TL;DR

This paper proves that within classical general relativity, static spherically symmetric traversable wormholes cannot be supported solely by classical scalar fields and nonexotic matter, requiring exotic matter for good asymptotic behavior.

Contribution

It establishes a no-go theorem showing that classical scalar fields and nonexotic matter cannot support well-behaved traversable wormholes in general relativity.

Findings

No static spherically symmetric traversable wormholes supported by classical scalar fields and nonexotic matter.

Good asymptotic behavior requires exotic matter violating null energy condition.

Results are independent of scalar field coupling, potential, and number of 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.