The shape of Scalar Gauss-Bonnet Gravity

Understand

We study the consistency of Scalar Gauss-Bonnet Gravity, a generalization of General Relativity where black holes can develop non-trivial hair by the action of a coupling $F(\Phi){\cal G}$ between a function of a scalar field and the Gauss-Bonnet invariant of the space-time.

• When properly normalized, interactions induced by this term are weighted by a cut-off, and take the form of an Effective Field Theory expansion.
• By invoking the existence of a Lorentz invariant, causal, local, and unitary UV completion of the theory, we derive positivity bounds for $n$-to-$n$ scattering amplitudes including exchange of dynamical gravitons.
• These constrain the value of all even derivatives of the function $F(\Phi)$, and are highly restrictive.