### Abstract:

We study the problem of the relativistic free electron gas at arbitrary degenerate electron
gas. The speci_c heat at constant volume and particle number cv and the speci_c heat
at constant pressure and particle number cp are calculated. The equation of state is also
studied. Non degenerate and degenerate electron limits are considered. We generalize the
formulas obtained in the non-relativistic and ultra-relativistic degenerate electron gas.
Neutron stars are much denser than white dwarf stars, which, once again, causes the
core of the stars to collapse. The compression of neutrons in the contracting core, however,
creates a neutron degenerate pressure. This pressure, analogous to the electron degenerate
pressure in white dwarf stars, combats the gravitational collapse of the star. If, however, the
neutron star is too massive (more than three solar masses), the neutron degenerate pressure
fails and the neutron star collapses into a black hole.
We now see that the role of both the neutron degenerate pressure, and the electron
degenerate pressure is crucial to the maintained stability of a star The energy corresponding
to this momentum, called the Fermi energy which we will discuss in the next section will also
increase. So, with a decreasing volume and an increasing particle momentum, we can say
that a pressure formed inside of the core of the star, and continues to increase as long as the
volume continues to increase, and that there are degenerate neutron energy states. Now that
we know where the pressure comes from, we can _nally derive a mathematical expression for
the neutron degeneracy pressure by non-relativistic neutrons inside of a neutron star.