LATE-TIME TAILS OF SELF-GRAVITATING SKYRMIONS

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 t(-4) at future timelike infinity and as 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.