Perturbation theory for self-gravitating gauge fields I: The odd-parity sector

Details Perturbation theory for self-gravitating gauge fields I: The odd-parity sector Perturbation theory for self-gravitating gauge fields I: The odd-parity sector

1999-10-18

arxiv.org/abs/gr-qc/9910059v1

Phys.Rev. D62 (2000) 084001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, revtex, no figures

Scientific paper

10.1103/PhysRevD.62.084001

A gauge and coordinate invariant perturbation theory for self-gravitating non-Abelian gauge fields is developed and used to analyze local uniqueness and linear stability properties of non-Abelian equilibrium configurations. It is shown that all admissible stationary odd-parity excitations of the static and spherically symmetric Einstein-Yang-Mills soliton and black hole solutions have total angular momentum number $\ell = 1$, and are characterized by non-vanishing asymptotic flux integrals. Local uniqueness results with respect to non-Abelian perturbations are also established for the Schwarzschild and the Reissner-Nordstr\"om solutions, which, in addition, are shown to be linearly stable under dynamical Einstein-Yang-Mills perturbations. Finally, unstable modes with $\ell = 1$ are also excluded for the static and spherically symmetric non-Abelian solitons and black holes.

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