Where and why does Einstein-scalar-Gauss-Bonnet theory break down?

In this talk, I will present a systematic exploration of the loss of predictivity in Einstein-scalar-Gauss-Bonnet (ESGB) gravity in spherical symmetry. I will first present a gauge covariant method of characterizing the breakdown of the hyperbolicity of the equations of motion in the theory. With this formalism, I will show that strong geodesic focusing leads to the breakdown of hyperbolicity, and the latter is unrelated to the violation of the null convergence condition. I then present numerical studies of the loss hyperbolicity of the equations during gravitational collapse for a version of the theory that admits "spontaneously scalarized'' black holes. I will devise a "phase space'' model to describe the end states for a given class of initial data. Using this phase space picture, I will demonstrate that the theory remains predictive (hyperbolic) for a range of GB couplings. The range of couplings, however, is small, and thus, the presence of "spontaneously scalarized'' solutions requires fine-tuning of initial data. These results, therefore, cast doubt as to whether scalarized black hole solutions can be realistically realized in Nature even if ESGB gravity happened to be the correct gravitational description.