A canonical two-scalar EFT cannot naturally produce supermassive-only black hole scalarization, because the generated G^2 term has the wrong sign and is suppressed.
Instead, asolutionwith ϕ“ 0isallowed if the metric is a solution of the theory L“ M 2 Pl 2 R` k 2 G2, k “ α2v2 m2 h Fp0q2
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Supermassive black hole scalarization and effective field theory
A canonical two-scalar EFT cannot naturally produce supermassive-only black hole scalarization, because the generated G^2 term has the wrong sign and is suppressed.