Instability of Einstein-Yang-Mills Solitons for Arbitrary Gauge Groups

Details Instability of Einstein-Yang-Mills Solitons for Arbitrary Gauge Groups Instability of Einstein-Yang-Mills Solitons for Arbitrary Gauge Groups

1994-01-19

arxiv.org/abs/gr-qc/9401019v1

Phys.Lett.B324:309-314,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, Latex, ZU-TH 4\94

Scientific paper

10.1016/0370-2693(94)90199-6

We prove that static, spherically symmetric, asymptotically flat, regular solutions of the Einstein-Yang-Mills equations are unstable for arbitrary gauge groups. The proof involves the following main steps. First, we show that the frequency spectrum of a class of radial perturbations is determined by a coupled system of radial "Schroedinger equations". Eigenstates with negative eigenvalues correspond to exponentially growing modes. Using the variational principle for the ground state it is then proven that there always exist unstable modes (at least for "generic" solitons). This conclusion is reached without explicit knowledge of the possible equilibrium solutions.

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