Late-Time Tails of Self-Gravitating Massless Fields

In this talk I summarize briefly recent results of joint work with P. Bizon, T. Chmaj and S. Zajac, on the nonlinear origin of the power law tails in the long-time evolution of self-gravitating massless fields. We focus on a spherically symmetric massless scalar field and wave map matter coupled to gravity. Using third-order perturbation method we derive explicit expressions for the tail (the decay rate and the amplitude) for solutions starting from small initial data and we verify this prediction via numerical integration of the full system of Einstein field equations. Our results show that the nonlinear effects can dominate the late time asymptotics. (author)