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We study the question of prompt vs. delayed collapse in the head-on collisionof two neutron stars. We show that the prompt formation of a black hole ispossible, contrary to a conjecture of Shapiro which claims that collapse isdelayed until after neutrino cooling. We discuss the insight provided byShapiro's conjecture and its limitation. An understanding of the limitation ofthe conjecture is provided in terms of the many time scales involved in theproblem. General relativistic simulations in the Einstein theory with the fullset of Einstein equations coupled to the general relativistic hydrodynamicequations are carried out in our study.Comment: 4 pages, 7 figure

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