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 unscalarized, has been recently proposed. We explore whether this model can emerge from an effective field theory obtained by integrating out a heavy second scalar field. We show that the resulting EFT 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 scalars. We show 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.