Late-time tails of self-gravitating skyrmions

TL;DR

This paper analyzes the long-time decay behavior of spherically symmetric solutions in the Einstein-Skyrme model, revealing decay rates and showing similarities with wave map models through nonlinear perturbation analysis.

Contribution

It provides the first leading order estimation of late-time tails in the Einstein-Skyrme model's trivial sector using nonlinear perturbation analysis.

Findings

Solutions decay as 1/t^4 at future timelike infinity.

Solutions decay as 1/u^2 at future null infinity.

Long-time tail behavior matches that of wave maps.

Abstract

We consider the long-time behaviour of spherically symmetric solutions in the Einstein-Skyrme model. Using nonlinear perturbation analysis we obtain the leading order estimation of the tail in the topologically trivial sector (B = 0) of the model. We show that solutions starting from small compactly supported initial data decay as 1/t^4 at future timelike infinity and as 1/u^2 at future null infinity. We also verified that long-time behaviour for the tail in Einstein-Skyrme model is exactly the same as it was obtained for wave maps.