Critical collapse in K-essence models

We study gravitational collapse in K-essence model with shift symmetry. For these models, we have the formation of two types of horizons, event and sonic. For the particular case K (X) = X + βX² we found three different regimes. In the weak field regime the scalar field disperses to infinity, in the very strong regime both horizons form at the same time and finally for the intermediate regime, the sonic horizon could form first or both horizons form at the same time. The threshold of formation of the horizon is found in the regime where the sonic horizon forms first. We observe a universal behavior with a scaling parameter γ ≃ 0.51. Interestingly this universal behavior is encoded in the sonic horizon even if an event horizon is expected to never form because of loss of hyperbolicity of the equations.