The shape of Scalar Gauss-Bonnet Gravity

TL;DR

This paper derives positivity bounds on Scalar Gauss-Bonnet Gravity, constraining the theory's parameters and challenging many existing models of black hole scalarization by ensuring consistency with a UV complete framework.

Contribution

It establishes new positivity bounds for Scalar Gauss-Bonnet Gravity, linking low-energy effective theory parameters to fundamental UV completion constraints.

Findings

Positivity bounds restrict the derivatives of the coupling function F(Φ).

Most models for black hole scalarization are ruled out by these bounds.

Some theory scales must be of Planckian order to satisfy the bounds.

Abstract

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. They require some of the scales of the theory to be of Planckian order, and rule out most of the models used in the literature for black hole scalarization.