Radial oscillations of homogeneous stellar objects and the critical value of adiabatic exponent

The criterion of stability against radial adiabatic oscillations is considered for the models of neutron homogeneous stars in the framework of general relativity. The critical value of adiabatic exponent $\gamma_{cr}$ is obtained in the framework of general relativity, which corresponds to the limit of stability of the star and is applicable in the whole allowable range where the parameter $\eta_1 =R/\alpha$ ($R$ – star radius, $\varepsilon$ – energy density, $\alpha=\sqrt{3c^4/(8\pi G\varepsilon)}$) varies. The obtained results are compared with the known result of Chandrasekhar.