Late-time tails of wave maps coupled to gravity

Abstract

We consider the late-time asymptotic behavior for solutions of Einstein's equations with the wave map matter. Using the third-order perturbation expansion about the flat spacetime we show that solutions starting from small compactly supported ℓ-equivariant initial data with ℓ ⩾ 1 decay as t−(2ℓ+2) at future timelike infinity and as u−(ℓ+1) at future null infinity.