Late-time tails of self-gravitating skyrmions

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.

7pp; revised version - title changed, sects. 2 and 3 replaced by the new version of sect. 2 with new figure added, section on numerics slightly modified, references updated, accepted for publication in Acta Phys. Pol. B