The shape of Scalar Gauss-Bonnet Gravity

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 $F(\Phi )\mathcal{G}$ 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.

34 pages, 3 figures. A comment on the effect of adding a mass and a self-coupling for the scalar field has been added. Matches journal version

References in corpus (21)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The Confrontation between General Relativity and Experiment
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Causality, Analyticity and an IR Obstruction to UV Completion
• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Healthy theories beyond Horndeski
• Gravitational Test Beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole
• Neutron-star mergers in scalar-tensor theories of gravity
• xPert: Computer algebra for metric perturbation theory
• Positive Moments for Scattering Amplitudes
• Self-interactions and Spontaneous Black Hole Scalarization
• Dynamics of spontaneous black hole scalarization and mergers in Einstein-scalar-Gauss-Bonnet gravity
• QED positivity bounds
• EHT tests of the strong-field regime of General Relativity
• Partial accretion in the propeller stage of low mass X-ray binary Aql X--1
• Positivity Bounds on Dark Energy: When Matter Matters
• Massless Positivity in Graviton Exchange
• Is the Standard Model in the Swampland? Consistency Requirements from Gravitational Scattering
• Scalar Fields Near Compact Objects: Resummation versus UV Completion

Cited by in corpus (12)

• Constraints on Einstein-dilaton-Gauss-Bonnet gravity from Black Hole-Neutron Star Gravitational Wave Events
• Fixing the dynamical evolution in scalar-Gauss-Bonnet gravity
• UV graviton scattering and positivity bounds from IR dispersion relations
• Constraining spontaneous black hole scalarization in scalar-tensor-Gauss-Bonnet theories with current gravitational-wave data
• Scalar Fields Near Compact Objects: Resummation versus UV Completion
• Positivity Bounds on parity-violating scalar-tensor EFTs
• Instability of scalarized compact objects in Einstein-scalar-Gauss-Bonnet theories
• Scalarization of isolated black holes in scalar Gauss-Bonnet theory in the fixing-the-equations approach
• Holographic Consistency and the Sign of the Gauss-Bonnet Parameter
• Constraints on Einstein-dilaton Gauss-Bonnet gravity with Taiji
• Mapping the Weak-Field Limit of Scalar-Gauss-Bonnet Gravity
• Radial perturbations of scalar-Gauss-Bonnet black holes beyond spontaneous scalarization