Gravitational collapse in SYK models and Choptuik-like phenomenon

SYK model is a quantum mechanical model of fermions which is solvable at strong coupling and plays an important role as perhaps the simplest holographic model of quantum gravity and black holes. The present work considers a deformed SYK model and a sudden quantum quench in the deformation parameter. The system, as in the undeformed case, permits a low energy description in terms of pseudo Nambu Goldstone modes. The bulk dual of such a system represents a gravitational collapse, which is characterized by a bulk matter stress tensor whose value near the boundary shows a sudden jump at the time of the quench. The resulting gravitational collapse forms a black hole only if the deformation parameter $\Delta\epsilon$ exceeds a certain critical value $\Delta\epsilon_c$ and forms a horizonless geometry otherwise. In case a black hole does form, the resulting Hawking temperature is given by a fractional power $T_{bh} \propto (\Delta\epsilon - \Delta\epsilon_c)^{1/2}$, which is reminiscent of the `Choptuik phenomenon' of critical gravitational collapse.