Abstract: Generic extensions of the standard model predict the existence of
ultralight bosonic degrees of freedom. Several ongoing experiments are
aimed at detecting these particles or constraining their mass range.
Here we show that massive vector fields around rotating black holes can
give rise to a strong superradiant instability, which extracts angular
momentum from the hole. The observation of supermassive spinning black
holes imposes limits on this mechanism. We show that current
supermassive black-hole spin estimates provide the tightest upper limits
on the mass of the photon (m(v) less than or similar to 4 X 10(-20) eV
according to our most conservative estimate), and that spin measurements
for the largest known supermassive black holes could further lower this
bound to m(v) less than or similar to 10(-22) eV. Our analysis relies on
a novel framework to study perturbations of rotating Kerr black holes in
the slow-rotation regime, that we developed up to second order in
rotation, and that can be extended to other spacetime metrics and other
theories.
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