Trapped ghosts: a new class of wormholes

TL;DR

This paper presents new static, spherically symmetric wormhole solutions in general relativity featuring a scalar field with a localized ghost region, revealing unique properties of such trapped-ghost wormholes.

Contribution

It introduces the concept of trapped-ghost wormholes with nonzero potentials and analyzes their properties, including mass and symmetry conditions.

Findings

Trapped-ghost wormholes require nonzero scalar potentials.

In asymptotically flat wormholes, the potential's sign alternates.

Mirror-symmetric wormholes have zero Schwarzschild mass at both ends.

Abstract

We construct examples of static, spherically symmetric wormhole solutions in general relativity with a minimally coupled scalar field $\phi$ whose kinetic energy is negative in a restricted region of space near the throat (of arbitrary size) and positive far from it. Thus in such configurations a "ghost" is trapped in the strong-field region, which may in principle explain why no ghosts are observed under usual conditions. Some properties of general wormhole models with the $\phi$ field are revealed: it is shown that (i) trapped-ghost wormholes are only possible with nonzero potentials $V(\phi)$; (ii) in twice asymptotically flat wormholes, a nontrivial potential $V(\phi)$ has an alternate sign, and (iii) a twice asymptotically flat wormhole which is mirror-symmetric with respect to its throat has necessarily a zero Schwarzschild mass at both asymptotics.