Abstract: The chart of nuclei could be enlarged with a branch describing neutron stars that are huge nuclei of a few solar masses held together by gravity force and sustained by the pressure due to the degenerate Fermi sea and repulsive nuclear forces. We contend that yet another branch could be added: objects with a large weak charge, with masses less than 10^−3 solar masses and having radii of a few meters, very compact, only slightly larger than their Schwarzchild radius, and sustained by the pressure generated by the weak force due to Z exchange. This interaction, insignificant in normal neutron stars, could become dominant when ultrahigh densities are reached due to the action of gravity and lead to stable configurations if the appropriate conditions are met. They would constitute a physical realization of the equation of state proposed by Zeldovich some decades ago.