Near-horizon pole configurations of a non-minimally coupled Proca field around a Schwarzschild black hole have critical masses μ r_- = √3 n, with the n=1 onset mass μ_c = √3/r_-.
Carter, inBlack Holes, Proceedings of 1972 Session of Ecole d’ete de Physique Theorique, edited by C
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Marginally stable Schwarzschild-black-hole-non-minimally-coupled-Proca-field bound-state configurations
Near-horizon pole configurations of a non-minimally coupled Proca field around a Schwarzschild black hole have critical masses μ r_- = √3 n, with the n=1 onset mass μ_c = √3/r_-.