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

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 asy...

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Published inClassical and quantum gravity Vol. 27; no. 17; p. 175003
Main Authors Bizoń, Piotr, Rostworowski, Andrzej, Zenginoğlu, Anıl
Format Journal Article
LanguageEnglish
Published IOP Publishing 07.09.2010
Subjects
Asymptotic properties
Basins
Borders
Dynamic tests
Dynamics
Evolution
Phases
Quantum gravity
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Summary: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 towards 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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ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/27/17/175003