Abstract
We investigate the late-time evolution of theYang-Mills field in the self-gravitating backgrounds:Schwarzschild and Reissner-Nordstrom spacetimes. Thelate-time power-law tails develop in the threeasymptotic regions: the future timelike infinity, thefuture null infinity and the black hole horizon. Inthese two backgrounds, however, the late-time evolutionhas quantitative and qualitative differences. In the Schwarzschild black hole background, thelate-time tails of the Yang-Mills field are the same asthose of the neutral massless scalar field withmultipole moment l = 1. The late-time evolutionis dominated by the spacetime curvature. When the backgroundis the Reissner-Nordstrom black hole, the late-timetails have not only a smaller power-law exponent, butalso an oscillatory factor. The late-time evolution is dominated by the self-interacting term ofthe Yang-Mills field. The cause responsible for thedifferences is revealed.
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Cai, RG., Wang, A. Late-time Evolution of the Yang-Mills Field in the Spherically Symmetric Gravitational Collapse. General Relativity and Gravitation 31, 1367–1382 (1999). https://doi.org/10.1023/A:1026737127191
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DOI: https://doi.org/10.1023/A:1026737127191