Solitons in a cavity for the Einstein-SU(2) Non-linear Sigma Model and Skyrme model

TL;DR

This paper constructs and analyzes new self-gravitating solitons within a cavity for the Einstein-SU(2) Non-linear Sigma and Skyrme models, revealing two solution branches with distinct properties and no spherically symmetric black holes under the given ansatz.

Contribution

It introduces a generalized ansatz to find self-gravitating solitons in a cavity for these models, identifying two solution branches and their characteristics.

Findings

Two branches of solutions with different parameter dependencies.

No spherically symmetric black hole solutions under the ansatz.

Solutions characterized by parameters like cavity size, redshift, energy, and charge.

Abstract

In this work, taking advantage of the Generalized Hedgehog Ansatz, we construct new self-gravitating solitons in a cavity with mirror-like boundary conditions for the SU(2) Non-linear Sigma Model and Skyrme model. For spherically symmetric spacetimes, we are able to reduce the system to three independent equations that are numerically integrated. There are two branches of well-behaved solutions. The first branch is defined for arbitrary values of the Skyrme coupling and therefore also leads to a gravitating soliton in the Non-linear Sigma Model, while the second branch exists only for non-vanishing Skyrme coupling. The solutions are quasi-static and in the first branch are characterized by two integration constants that correspond to the frequency of the phase of the Skyrme field and the value of the Skyrme profile at the origin, while in the second branch the latter is the unique parameter characterizing the solutions. These parameters determine the size of the cavity, the redshift at the boundary of the cavity, the energy of the scalar field and the charge associated to a U(1) global symmetry. We also show that within this ansatz, assuming analyticity of the matter fields, there are no spherically symmetric black hole solutions.