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2022

Schwarzschild quasi-normal modes of non-minimally coupled vector fields

Garcia-Saenz, Sebastian, Held, Aaron, Zhang, Jun

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We study perturbations of massive and massless vector fields on a Schwarzschild black-hole background, including a non-minimal coupling between the vector field and the curvature.

The coupling is given by the Horndeski vector-tensor operator, which we show to be unique, also when the field is massive, provided that the vector has a vanishing background value.
We determine the quasi-normal mode spectrum of the vector field, focusing on the fundamental mode of monopolar and dipolar perturbations of both even and odd parity, as a function of the mass of the field and the coupling constant controlling the non-minimal interaction.
In the massless case, we also provide results for the first two overtones, showing in particular that the isospectrality between even and odd modes is broken by the non-minimal gravitational coupling.

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