Neutron stars are formed from the gravitational collapse of the inner core of a large star following a supernova explosion. The inner core must be between 1.4 and 3 solar masses for a neutron star to form after the explosion, any greater and a black hole will form instead. Thus neutron stars weigh between 1.4 and 3 solar masses, but the majority weigh between 1.31 and 1.39 solar masses. Newly created black holes are between 3 and 5 solar masses. Those larger that 5 solar masses have grown from smaller ones by accretion. The extremely strong gravitational force squeezes the electrons of the atoms inside the protons in the nucleus, turning them into neutrons to join the other neutrons already there. This is similar to inverse beta decay, and anti-neutrinos are emitted, 1057 of them within 10 seconds. This blasts the outer layers of the star apart. See neutrinos
The 1057 neutrons in a neutron star are bound together mainly by gravitational attraction unlike those in a nucleus which are bound by the strong nuclear force and which is insufficient to bind even 2 neutrons together. (The attractive force between two different nucleons is only weak; the binding energy of the proton to the neutron in deuterium nuclei is only 2MeV per nucleon, it is thus only weakly bound and is much larger in size than an alpha particle, the most strongly bound nuclear cluster. But when protons and neutrons gather in greater numbers than three, the binding energy per nucleon reaches a saturation value of about 8MeV). However, in the depths of a neutron star, the long-range interaction between neutrons is strong enough to bind them in pairs, forming a superfluid boson state.
Neutron stars have a high peculiar velocity, enough to escape the galaxy in which they were born. When a neutron star is born, it emits huge numbers of neutrinos in all directions, but if just 1% more were emitted in one favoured direction, this would jet-propel it like a rocket. The asymmetry may arise when, under the intense magnetic field, some electron neutrinos travelling with the field in one direction were preferentially changed into - and-neutrinos by the magnetic field. Because, under the extreme density, the - and-neutrinos can escape easier than electron neutrinos, this would propel the neutron star.
The characteristic measure of the size of relativistic effects in a celestial body is GM/Rc2, where G is the Universal constant of gravitation, c the speed of light, M the mass of the body, and R the radius of the body. For the sun this factor is 10-5; for a white dwarf is 10-3; but for a neutron star is as high as 0.3, so a neutron star experiences relativistic effects placing a maximum size and rotation rate on a neutron star. For a black hole it is 1.