Strong Hyperbolicity and Nonradial Quasinormal Modes of Quartic SU(2) Proca Black Holes

ABSTRACT We derive the generic higher multipole perturbation theory of asymptotically flat branch I black holes in quartic SU(2) Proca theory. The static geometry depends only on , but nonspherical perturbations resolve the independent ratio . A constraint analysis before harmonic reduction identifies eleven physical modes and shows that the reduced physical principal system at finite radius is locally strongly hyperbolic precisely for . Diagonal rotation harmonics divide these modes into six axial and five polar amplitudes. We derive both coupled radial systems including their Proca and Einstein constraints. One polar channel decouples exactly, with exterior potential ; an energy identity therefore excludes every exponentially growing quasinormal mode in that channel. After analytic extraction of the ingoing and outgoing phases, the remaining equations form boundary regular polynomial eigenvalue problems. Their fundamental spectra lift the background coupling degeneracy and reproduce the Schwarzschild spin one and spin two limits of all transverse families. Longitudinal limits instead retain the expected path dependence where local Yang–Mills symmetry is restored; because their local kinetic matrix degenerates as the magnetic background vanishes, we interpret those longitudinal frequencies as fixed multipole reduced spectral resonances. Resolution convergence, independent endpoint recurrences, off grid equation residuals, and Regge–Wheeler and Zerilli regressions validate the resolved spectra. All resolved coupled fundamental families are damped over the sampled frequency and parameter domains; only the decoupled channel carries an analytic mode stability theorem.

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