content_image/334623.jpg content_image/334624.jpg
where the ultrarelativistic limit of Eq. (18) has been used in the kinetic term. One can immediately see that the electrostatic and gravitational contributions become equal at 

<img src='content_image/334623.jpg'>

where the value ξ = 1 / 38 was used for the estimation. The corresponding mass M$_{min}$ = N$_{min}$m$_{B}$ is about 10 13 g, i. e. almost 20 orders of magnitude smaller than the maximum mass of a neutron star. At N$_{B}$ < N$_{min}$ there exists no equilibrium configurations because the kinetic pressure will force the system to expand indefinitely. 

At N$_{B}$ > N$_{min}$ the negative gravitational contribution exceeds the electrostatic one. The latter becomes completely negligible and can be neglected at baryon numbers ∼ 10 57 characteristic for compact stars. As was first demonstrated by Chandraseckhar [22] and Landau [23], a compact star can be stabilized by the pressure of a degenerate fermion gas alone. From (22) one can see that the balance between kinetic and gravitational energy can be achieved if the total number of baryons is smaller than 

<img src='content_image/334624.jpg'>

As follows from this simple calculations, the corresponding maximum mass of a neutron star, M$_{max}$ = N$_{max}$m$_{n}$ is about 3.2 M ⊙ . Numerical calculations within General Relativity [24] for the degenerate noninteracting neutron gas predict somewhat lower maximum mass, M$_{max}$ = 0 . 7 M ⊙ . The repulsive neutron-neutron interaction may increase this value up to 4 M ⊙ (see e.g. ref.[25]). It is easy to see that stars with N$_{min}$ < N$_{B}$ < N$_{max}$ have a stable equilibrium state. Indeed, Eq. (22) shows that in this case W ( R ) > 0 and changes as 1 /R , so that the star should expand to lower densities. But this expansion will terminate at a large enough R , when the neutron gas becomes non-relativistic. As follows from Eq. (18), in this limit the energy per particle is m$_{n}$ + 3 k 2 $_{Fn}$/ 10 m$_{n}$ , i. e. changes as 1 /R 2 at large R . Since the negative gravitational contribution still changes as 1 /R , it wins so that the total energy per baryon approaches m$_{n}$ from below. Therefore a minimum develops in W ( R ). This is famous Landau’s argument presented in ref. [23]. In ref. [25] it was reformulated for the case of General Relativity and for an arbitrary fermion mass. 

It is clear now that ignoring the kinetic-energy term in Eq. (22), as done in ref. [7], will lead to the erroneous conclusion regarding the star stability. Although the electrostatic and gravitational forces can balance each other at N$_{B}$ = N$_{min}$ , this state corresponds to 

