Scalar fields as sources for wormholes and regular black holes

TL;DR

This paper reviews static, spherically symmetric solutions in general relativity involving scalar fields, focusing on wormholes and regular black holes, their stability, and the role of ghost fields with negative kinetic energy.

Contribution

It introduces the concept of 'trapped ghost' scalar fields, general theorems on black hole structures, and analyzes stability via effective potential shapes near wormhole throats.

Findings

Scalar fields can support wormholes and regular black holes without singularities.

Stability analysis reveals universal effective potential shapes near throats and transition surfaces.

Ghost fields may be confined or decay rapidly, explaining their observational absence.

Abstract

We review nonsingular static, spherically symmetric solutions of general relativity with a minimally coupled scalar field $\phi$ as a source. Considered are wormholes and regular black holes without a center, including black universes (black holes with an expanding cosmology beyond the horizon). Such configurations require a "ghost" field with negative kinetic energy, but it may be negative in a restricted (strong-field) region of space and positive outside it ("trapped ghost") thus explaining why no ghosts are observed under usual conditions. Another possible explanation of the same may be a rapid decay of a ghost field at large radii. Before discussing particular examples, some general results are presented, such as the necessity of anisotropic matter for obtaining asymptotically flat or anti-de Sitter wormholes, no-hair and global structure theorems for black holes with scalar fields. The stability properties of scalar wormholes and regular black holes are discussed for perturbations preserving spherical symmetry. It is stressed that the effective potential $V_{eff}$ for perturbations has universal shapes near generic wormhole throats (a positive pole regularizable by a Darboux transformation) and near transition surfaces from canonical to ghost behavior of the scalar field (a negative pole at which the perturbation finiteness requirement plays a stabilizing role). It is also found that positive poles of $V_{eff}$ emerging at "long throats" (with the spherical radius $r \approx r_0 + {\rm const} \cdot x^{2n}$, $n > 1$, if $x=0$ is the throat) may be regularized by repeated Darboux transformations for some values of $n$.