Constraining strongly-warped extra dimensions with rotating black holes

Massive bosonic fields can trigger superradiant instabilities in rotating astrophysical black holes leading to gaps in their mass-spin distribution. For spin-2 fields, the instability timescale is orders of magnitude shorter than for any other superradiant mode, thereby yielding much stronger constraints. We consider a tower of ultra-light spin-2 fields arising from a warped compactification of a single extra dimension and translate superradiant constraints on their masses into constraints on the warping. As a concrete scenario we consider the 2-brane Randall-Sundrum model and find constraints on the size of the extra dimension and the curvature of $AdS_5$. We discuss the implications of these bounds for strongly warped throats and D-brane uplifts commonly used in attempts to realise metastable de Sitter vacua in string theory.