Question

Why is there an upper limit to the mass of neutron stars?

Answer 1

There is an upper limit on the mass of a neutron star because of neutron degeneracy pressure.

Explanation:

Neutrons are fermions. This means that they obey the Fermi-Dirac statistics and the Pauli Exclusion principle. This means that no two neutrons can be in the same quantum state at the same time.

If a neutron star has a mass of about 3 solar masses or more, gravity is in control. The Pauli Exclusion principle has an associated neutron degeneracy pressure. If this pressure is exceeded the quantum effects can't keep the neutrons in separate states.

Once the neutron degeneracy pressure is exceeded, then the neutrons have to collapse into a more degenerate state, namely a black hole.