Late-time tails of a Yang-Mills field on Minkowski and Schwarzschild backgrounds

Bizon, Piotr; Chmaj, Tadeusz; Rostworowski, Andrzej

doi:10.1088/0264-9381/24/13/F01

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Late-time tails of a Yang-Mills field on Minkowski and Schwarzschild backgrounds

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Bizon, Piotr
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0704.0993v2.pdf
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cqg7_13_f01.pdf
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Citation

Bizon, P., Chmaj, T., & Rostworowski, A. (2007). Late-time tails of a Yang-Mills field on Minkowski and Schwarzschild backgrounds. Classical and Quantum Gravity, 24(13), F55-F63. doi:10.1088/0264-9381/24/13/F01.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4912-A

Abstract

We study the late-time behavior of spherically symmetric solutions of the Yang-Mills equations on Minkowski and Schwarzschild backgrounds. Using nonlinear perturbation theory we show in both cases that solutions having smooth compactly supported initial data posses tails which decay as $t^{-4}$ at timelike infinity. Moreover, for small initial data on Minkowski background we derive the third-order formula for the amplitude of the tail and confirm numerically its accuracy.