The dynamics of spherically symmetric black holes in scalar-Gauss-Bonnet gravity with a Ricci coupling

We study the dynamics of spherically symmetric black holes in scalar Gauss-Bonnet gravity with an additional coupling between the scalar field and the Ricci scalar using non-linear simulations that employ excision. In this class of theories, black holes possess hair if they lie in a specific mass range, in which case they exhibit a finite-area singularity, unlike general relativity. Our results show that the Ricci coupling can mitigate the loss of hyperbolicity in spherical evolution with black hole initial data. Using excision can enlarge the parameter space for which the system remains well-posed, as one can excise the elliptic region that forms inside the horizon. Furthermore, we explore a possible relation between the loss of hyperbolicity and the formation of the finite-area singularity inside the horizon. We find that the location of the singularity extracted from the static analysis matches the location of the sonic line well. Finally, when possible, we extract the monopolar quasi-normal modes and the time scale of the linear tachyonic instability associated with scalarization. We also check our results by utilizing a continued fraction analysis and supposing linear perturbations of the static solutions.