General Relativistic Solitons (II)

TL;DR

This paper explores the existence of non-topological solitons in extended Einstein theories with scalar, Maxwell, and dilaton fields, finding that dilaton boundary conditions cannot be satisfied, but solitonic structures exist without it.

Contribution

It introduces a simple extension of Einstein theory with a non-linear scalar field and examines soliton solutions, highlighting the role of the dilaton and non-linear potential.

Findings

Dilatonic boundary conditions cannot be satisfied.

Solitonic structures exist without the dilaton.

Excited states have a discrete mass spectrum.

Abstract

We investigate the possible existence of non-topological solitons in string-like theories, or in other completions of Einstein theory, by examining a simple extension of standard theory that describes a non-linear scalar field interacting with the Einstein, Maxwell and Weyl (dilaton) fields. The Einstein and Maxwell couplings are standard while the dilatonic coupling is taken to agree with string models. The non-linear scalar potential is quite general. It is found to be impossible to satisfy the dilatonic boundary conditions. Excluding the dilaton field we find a variety of solitonic structures differing in ways that depend on the non-linear potential. In general the excited states exhibit a discrete mass spectrum. At large distances the gravitational field approaches the Reissner-Nordstrom solution.