Hyperbolicity in Spherical Gravitational Collapse in a Horndeski Theory
  We numerically study spherical gravitational collapse in shift symmetric
Einstein dilaton Gauss Bonnet (EdGB) 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 evolution of the system, treated as a hyperbolic initial
boundary value problem, leads to the equations of motion becoming ill-posed
when the elliptic region forms. No singularities or discontinuities are
encountered on the corresponding effective "Cauchy horizon". Therefore it is
conceivable that a well-posed formulation of EdGB gravity (at least within
spherical symmetry) may be possible if the equations are appropriately treated
as mixed-type.
