We study the effects of treating the equilibrium of a white dwarf within general relativity. We approximate the electron gas within the star with an ideal, perfect, degenerate one. We determine the magnitude of the correction on the Newtonian (Chandrasekhar) limiting mass for central densities approaching the neutron drip critical one. We also discuss the effect of considering a temperature gradient within the star interior due to heat transfer. We point out that, whereas the degenerate hypothesis is fully legitimate, dropping the ideal and perfect assumption may lead to observable effects. This would require a careful study of the Jellium ground state on curved spacetime.