Late-time evolution of the Yang-Mills field in the spherically symmetric gravitational collapse

We investigate the late-time evolution of the Yang-Mills field in the selfgravitating backgrounds: Schwarzschild and Reissner-Nordström spacetimes. The late-time power-law tails develop in the three asymptotic regions: the future timelike infinity, the future null infinity and the black hole horizon. In these two backgrounds, however, the late-time evolution has quantitative and qualitative differences. In the Schwarzschild black hole background, the late-time tails of the Yang-Mills field are the same as those of the neutral massless scalar field with multipole moment l = 1. The late-time evolution is dominated by the spacetime curvature. When the background is the ReissnerNordström black hole, the late-time tails have not only a smaller power-law exponent, but also an oscillatory factor. The late-time evolution is dominated by the self-interacting term of the Yang-Mills field. The cause responsible for the differences is revealed. PACS numbers: 04.20.Ex, 04.30.Nk, 04.40.-b, 04.70.Bw Typeset using REVTEX