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 self gravitating backgrounds: Schwarzschild and Reissner-Nordstrom spacetimes. T he late-time power-law tails develop in the three asymptotic regions: the f uture timelike infinity, the future null infinity and the black hole horizo n. In these two backgrounds, however, the late-time evolution has quantitat ive and qualitative differences. In the Schwarzschild black hole background , the late-time tails of the Yang-Mills held are the same as those of the n eutral massless scalar field with multipole moment l = 1. The late-time evo lution is dominated by the spacetime curvature. When the background is the Reissner-Nordstrom 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 cau se responsible for the differences is revealed.