Criticality in Einstein-Gauss-Bonnet Gravity: Gravity without Graviton

TL;DR

This paper investigates a critical point in Einstein-Gauss-Bonnet gravity where the usual graviton modes disappear, yet black hole solutions persist due to nonlinear effects, revealing novel phenomena in higher derivative gravities.

Contribution

It identifies critical points in Einstein-Gauss-Bonnet and extended quadratic curvature gravities where linear graviton modes vanish, highlighting new nonlinear gravitational phenomena.

Findings

At the critical point, linear perturbations lack kinetic terms.

Black hole solutions exist despite the absence of linear graviton modes.

Critical phenomena are likely common in higher derivative gravity theories.

Abstract

General Einstein-Gauss-Bonnet gravity with a cosmological constant allows two (A)dS spacetimes as its vacuum solutions. We find a critical point in the parameter space where the two (A)dS spacetimes coalesce into one and the linearized perturbations lack any bilinear kinetic terms. The vacuum perturbations hence loose their interpretation as linear graviton modes at the critical point. Nevertheless, the critical theory admits black hole solutions due to the nonlinear effect. We also consider Einstein gravity extended with general quadratic curvature invariants and obtain critical points where the theory has no bilinear kinetic terms for either the scalar trace mode or the transverse modes. Such critical phenomena are expected to occur frequently in general higher derivative gravities.