The shape of scalar Gauss-Bonnet gravity

A bstract We study the consistency of Scalar Gauss-Bonnet Gravity, a generalization General Relativity where black holes can develop non-trivial hair by action coupling F (?) $$ \mathcal{G} G between function scalar field and invariant space-time. When properly normalized, interactions induced this term are weighted cut-off, take form an Effective Field Theory expansion. By invoking existence Lorentz invariant, causal, local, unitary UV completion theory, we derive positivity bounds for n -to- scattering amplitudes including exchange dynamical gravitons. These constrain value all even derivatives (?), highly restrictive. They require some scales theory to be Planckian order, rule out most models used in literature hole scalarization.