Blowup/scattering alternative for a discrete family of static critical solutions with various number of unstable eigenmodes

Donets, Evgeny E.; Hayryan, Edik A.; Streltsova, Oksana I.

Blowup/scattering alternative for a discrete family of static critical solutions with various number of unstable eigenmodes

Authors

Donets, Evgeny E.

Hayryan, Edik A.

Streltsova, Oksana I.

Description

Decay of regular static spherically symmetric solutions in the SU(2) Yang-Mills-dilaton (YMd) system of equations under the independent excitation of their unstable eigenmodes has been studied self-consistently in the nonlinear regime. The considered regular YMd solutions form a discrete family and can be parametrised by the number $N=1,2,3,4...$ of their unstable eigenmodes in linear approximation. We have obtained strong numerical evidences in favour of the following statements: i) all static YMd solutions are distinct local threshold configurations, separating blowup and scattering solutions; ii) the main unstable eigenmodes are only those responsible for the blowup/scattering alternative; iii) excitation of higher unstable eigenmodes always leads to finite-time blowup; iv) the decay of the lowest N=1 static YMd solution via excitation of its unique unstable mode is an exceptional case because the resulting waves propagate as a whole without energy dispersion revealing features peculiar to solitons. Applications of the obtained results to Type-I gravitational collapse of massless fields are briefly discussed.
29 pages, 10 figures