We shall show in this report that the theoretical evolution of a particular class of systems containing a neutron star, the so-called black widow binaries, suggest masses above the∼2M⊙, a fact that would bring serious concerns about the right description of the equation of state above the saturation density. Moreover, so far the actual determinations of masses for these systems consistently give values above2M⊙, reinforcing the quandary. In this sense, and given that the confirmation of these ideas would create problems for the microphysical description, we argue that a crisis could be in the works in neutron star physics