<p>We present calculations concerning the mass of various compact objects such as white dwarfs or neutron stars at zero temperature. To this end, we revisit the seminal work of Chandrasekhar, which is extended from the Newtonian equation of hydrostatic equilibrium to the relativistic regime using general relativity. The role of the kinetic energy density of the electrons as well as their rest-mass in the equation of state is discussed. If we use general relativity or include the kinetic energy density of the electrons and their rest-mass, it is shown numerically that the mass, as a function of a useful parameter related to the Fermi momentum and thus to the central mass density of the compact object, reaches a maximum and then shows a damped-oscillating behavior around a saturation mass obtained at large density. These results depart notably from the well-known solution of Chandrasekhar, which used Newtonian equation of hydrostatic equilibrium and surprisingly neglected the kinetic energy density of the electrons as well as their rest-mass while using their relativistic pressure in the equation of state. We then propose an equation of state that takes into account neutronization to have a smooth transition between white dwarfs and neutron stars using general relativity. Shortcomings of such an approach are discussed based on numerical results.</p>