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We consider the head-on collision of equal-mass neutron stars boosted towardseach other and we study the behavior of such systems near the threshold ofblack-hole formation. In particular, we confirm the previous findings by [1]that a type-I critical phenomenon can be observed by fine-tuning the initialmass of the two neutron stars. At the same time, we argue against theinterpretation that the critical solution is not a perturbed spherical star andshow instead that the metastable star corresponds to a (perturbed) equilibriumsolution on the unstable branch of the equilibrium configurations. As a result,the head-on collision of two neutron stars near the critical threshold can beseen as a transition in the space of configurations from an initial stablesolution over to a critical metastable one which can either migrate to a stablesolution or collapse to a black hole. The critical exponent for this processshows a fine structure which was already observed in the case of the criticalcollapse of scalar fields but never before for perfect fluids.

Critical Phenomena in Neutron Stars II: Head-on Collisions