Global Existence and Singularity Formation of Classical Solutions in Einstein-Skyrme System

TL;DR

This paper investigates the conditions under which classical solutions to the Einstein-Skyrme system exist globally or develop singularities, focusing on spherical symmetry and dynamic fields without potential terms.

Contribution

It provides criteria for the existence of global smooth solutions and analyzes singularity formation within the Einstein-Skyrme system under spherical symmetry.

Findings

Existence of unique smooth solutions for finite time with arbitrary initial data.

Conditions under which solutions can be extended to infinity.

Configurations leading to singularities at the coordinate origin.

Abstract

In this paper, we elucidate the problem of gravitating Skyrmion governed by field equations of the Einstein-Skyrme system with no potential term in the Bondi coordinate. The spherical symmetry has to be assumed and both the metric functions and Skyrme ansatz depend on radial and retarded time coordinates which implies that the system is dynamic. We show that unique smooth solutions with arbitrary initial data exist for a certain time interval with the extra condition that the time interval must be finite in order to have a non-zero topological charge. Then, the strategy to show that global smooth solutions exist is to restrict the initial data and proceed to find suitable configurations for extending the time interval to infinity. We also discuss the possible configurations within The Einstein-Skyrme System which develop singularities in coordinate origin.