Hyperbolicity in gravitational collapse in a modified gravity theory

We numerically study spherical gravitational collapse in a modified gravity theory, Truncated Einstein dilaton Gauss Bonnet (TEdGB) gravity. We find evidence that there are open sets of initial data for which the character of the system of equations changes from hyperbolic to elliptic type in a compact region of the spacetime. In these cases the evolution of the system, treated as a hyperbolic initial boundary value problem, develops a region where the equations of motion become ill-posed. No singularities or discontinuities are encountered on the corresponding effective "Cauchy horizon". Therefore it is not implausible that a well-posed formulation of TEdGB gravity (at least within spherical symmetry) may be possible if the equations are appropriately treated as mixed-type.