Shapiro conjecture: Prompt or delayed collapse in the head-on collision of neutron stars?

We study the question of prompt versus delayed collapse in the head-on collision of two neutron stars. We show that the prompt formation of a black hole is possible, contrary to a conjecture of Shapiro which claims that collapse is delayed until after neutrino cooling. An understanding of the limitation of the conjecture is provided in terms of the many time scales involved in the problem. General relativistic simulations with the full set of Einstein equations coupled to the general relativistic hydrodynamic equations are carried out.