Nonlinear evolution in extended scalar-Gauss-Bonnet gravity

Abstract Scalar-Gauss-Bonnet (sGB) gravity with a coupling between the scalar field and the Ricci scalar displays interesting properties, including black hole stability, agreement with the binary pulsar constraints, and compatibility with general relativity as a cosmological late-time attractor. Previous studies have shown that spherical collapse in this framework is well-posed over a wide parameter range. Here, we extend this analysis to examine 3 + 1 evolution for static and rotating black holes, confirming that the evolution remains hyperbolic if the weak coupling condition is not strongly violated. Hyperbolicity loss is linked to the gravitational sector of the physical modes, rather than the gauge choice. Our results also indicate that stationary, near-extremal scalarized black holes may exist in the Ricci-coupled sGB theory for a large enough region of the parameter space with the scalar field sourced by the spacetime curvature instead of the black hole spin.