Supermassive black hole scalarization and effective field theory

A model in which black hole scalarization occurs for supermassive black holes, while their less massive counterparts remain nonscalarized, has been recently proposed. We explore whether this model can emerge in a variety of settings. First, we consider an effective field theory obtained by integrating out a heavy second scalar field. We show that the resulting effective field theory does not have the right coupling sign or the right hierarchy of scales. We then consider whether supermassive black hole scalarization could occur in theories with two (possibly light) scalars, and find that although they can violate black hole uniqueness through curvature- and spin-induced scalarization, they do not naturally produce scalarization exclusively for supermassive black holes. Finally, we assess whether a Higgs-type mechanism could enable supermassive black hole scalarization, and identify regions of parameter space where this is indeed possible.