Abstract
We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-AdS black-hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in an excellent agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.
Highlights
Introduction.—Maxwell equations describe a theory of a massless vector field
We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-AdS black-hole spacetimes in any number of dimensions, filling a long-standing gap in the literature
The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated
Summary
Three independent polarizations of the Proca field and that we are able to much more effectively reconstruct the unstable modes recently studied in [9] by heavy numerical methods. We conclude with some general remarks on possible future directions. Spacetime geometry.—In what follows we want to demonstrate the separability of the four- and higherdimensional Proca equations in the background of a wide class of metrics that include the general Kerr-NUT-AdS solutions [17] as a special case. Such a separability is valid in both even and odd dimensions; the forms of the metric and of the separated equations are slightly different. In this Letter we restrict to the case of even dimensions, D 1⁄4 2N
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