Hyperbolicity in scalar-Gauss-Bonnet gravity: A gauge invariant study for spherical evolution

We study spherical evolution in scalar-Gauss-Bonnet gravity with additional Ricci coupling and use the gauge-invariant approach introduced recently by Reall to track well-posedness. Our results show that loss of hyperbolicity when it occurs, is due to the behavior of physical degrees of freedom. They provide further support to the idea that this behavior can be tamed by additional interactions of the scalar. We also point out a limitation of this gauge-invariant approach: the fact that field redefinitions can change the character of the evolution equations.