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We demonstrate the separability of the massive vector (Proca) field equationin general Kerr-NUT-(A)dS black hole spacetimes in any number of dimensions,filling a long-standing gap in the literature. The obtained separated equationsare studied in more detail for the four-dimensional Kerr geometry and thecorresponding quasinormal modes are calculated. Two of the three independentpolarizations of the Proca field are shown to emerge from the separation ansatzand the results are found in a perfect agreement with those of the recentnumerical study where the full coupled partial differential equations weretackled without using the separability property.

Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes