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Anomalous decay rate of quasinormal modes

The decay timescales of the quasinormal modes of a massive scalar field have an intriguing behavior: they either grow or decay with increasing angular harmonic numbers $\ell$, depending on whether the mass of the scalar field is small or large. We identify the properties of the effective potential of the scalar field that leads to this behavior and characterize it in detail. If the scalar field is non-minimally coupled, considered here, the scalar quasinormal modes will leak into the gravitational wave signal and will have decaying times that are comparable or smaller than those typical in General Relativity. Hence, these modes could be detectable in the future. Finally, we find that the anomalous behavior in the decay timescales of quasinormal modes is present in a much larger class of models beyond a simple massive scalar field.