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

@article{Bizon2007LatetimeTO,
  title={Late-time tails of a Yang–Mills field on Minkowski and Schwarzschild backgrounds},
  author={Piotr Bizo'n and Tadeusz Chmaj and Andrzej Rostworowski},
  journal={Classical and Quantum Gravity},
  year={2007},
  volume={24},
  pages={F55 - F63}
}
We study the late-time behaviour 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 possess 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 numerically confirm its accuracy. 
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References

SHOWING 1-10 OF 15 REFERENCES

Late-time Evolution of the Yang-Mills Field in the Spherically Symmetric Gravitational Collapse

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…

The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space

In this paper and its sequel we shall prove the local and then the global existence of solutions of the classical Yang-Mills-Higgs equations in the temporal gauge. This paper proves local existence…

Asymptotic properties of the solutions of linear and nonlinear spin field equations in Minkowski space

In this paper I will first derive, based on energy estimations and geometric invariance, the asymptotic behavior of solutions of linear spin field equations in Minkowski space. It generalizes the…

Spectral decomposition of the perturbation response of the Schwarzschild geometry.

  • Leaver
  • Physics, Mathematics
    Physical review. D, Particles and fields
  • 1986
The branch-cut integral produces a weak late-time radiative power-law decay tail that will characterize the astrophysically observed radiation spectrum for times subsequent to the exponential decay of the quasinormal ringing.

The Yang-Mills equations on the universal cosmos

Finite energy solutions of the Yang-Mills equations in $\mathbb{R}^{3+1}$

Yang-Mills equations in R3+1 is well-posed in the energy norm. This means that for an appropriate gauge condition, we construct local, unique solutions in a time interval which depends only on the…

Global existence of solutions of the Yang–Mills equations on globally hyperbolic four dimensional Lorentzian manifolds

We prove global solvability of the Cauchy problem for the Yang-Mills equations on smooth globally hyperbolic four dimensional Lorentzian manifolds.

Space-time symmetries in gauge theories

A general definition of symmetries of gauge fields is proposed and a method developed for constructing symmetric fields for an arbitrary gauge group. Scalar fields occur naturally in the formalism…

The scattering of certain Yang-Mills fields

The Yang-Mills fields considered by us in an earlier paper are asymptotically non-interacting. Also any free field is an incoming field for some Yang-Mills field.

Asian J

  • Math. 1, 530
  • 1997