Wormholes supported by chiral fields

TL;DR

This paper explores static, spherically symmetric wormhole solutions in general relativity supported by chiral scalar fields from nonlinear sigma models, revealing conditions for wormholes and horizons depending on the target space metric.

Contribution

It demonstrates that chiral fields can support wormholes and horizons, extending the understanding of scalar field configurations in gravitational solutions.

Findings

Wormholes can be supported by chiral scalar fields with specific target space metrics.

Schwarzschild solutions can correspond to trivial chiral field configurations with zero stress-energy.

Explicit examples of chiral field configurations and their properties are provided.

Abstract

We consider static, spherically symmetric solutions of general relativity with a nonlinear sigma model (NSM) as a source, i.e., a set of scalar fields $\Phi = (\Phi^1,...,\Phi^n)$ (so-called chiral fields) parametrizing a target space with a metric $h_{ab}(\Phi)$. For NSM with zero potential $V(\Phi)$, it is shown that the space-time geometry is the same as with a single scalar field but depends on $h_{ab}$. If the matrix $h_{ab}$ is positive-definite, we obtain the Fisher metric, originally found for a canonical scalar field with positive kinetic energy; otherwise we obtain metrics corresponding to a phantom scalar field, including singular and nonsingular horizons (of infinite area) and wormholes. In particular, the Schwarzschild metric can correspond to a nontrivial chiral field configuration, which in this case has zero stress-energy. Some explicit examples of chiral field configurations are considered. Some qualitative properties of NSM configurations with nonzero potentials are pointed out.