Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime

Details Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime Saddle-point dynamics of a Yang-Mills field on the exterior Schwarzschild spacetime

2010-05-11

arxiv.org/abs/1005.1708v1

Class.Quant.Grav.27:175003,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 5 figures

Scientific paper

10.1088/0264-9381/27/17/175003

We consider the Cauchy problem for a spherically symmetric SU(2) Yang-Mills field propagating outside the Schwarzschild black hole. Although solutions starting from smooth finite energy initial data remain smooth for all times, not all of them scatter since there are non-generic solutions which asymptotically tend to unstable static solutions. We show that a static solution with one unstable mode appears as an intermediate attractor in the evolution of initial data near a border between basins of attraction of two different vacuum states. We study the saddle-point dynamics near this attractor, in particular we identify the universal phases of evolution: the ringdown approach, the exponential departure, and the eventual decay to one of the vacuum states.

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