STABILITY ANALYSIS OF NEW SOLUTIONS OF THE EYM SYSTEM WITH A COSMOLOGICAL CONSTANT

We analyze the stability properties of the purely magnetic, static sol utions to the Einstein-Yang-Mills equations with a cosmological consta nt. It is shown that all three classes of solutions found in a recent study are unstable under spherical perturbations. Specifically, we arg ue that the configurations have n unstable modes in each parity sector , where n is the number of nodes of the magnetic Yang-Mills amplitude of the background solution. The ''sphaleronlike'' instabilities (odd p arity modes) decouple from the gravitational perturbations. They are o btained from a regular Schrodinger equation after a supersymmetric tra nsformation. The body of the work is devoted to the fluctuations with even parity. The main difficulty arises because the Schwarzschild gaug e, which is usually imposed to eliminate the gravitational perturbatio ns from the Yang-Mills equation, is not regular for solutions with com pact spatial topology. In order to overcome this problem, we derive a gauge-invariant formalism by virtue of which the unphysical (gauge) mo des can be isolated.