The role of three-body force (TBF) and the relativistic corrections (RC) on the equations of state of nuclear matter and β-stable matter (BSM) within the relativistic lowest-order constrained variation (RLOCV) approach are studied. The AV14 potential and its relativistic version (˜v14 ) as well as the AV18 potential are considered as the bare two-body potentials by employing the nuclear many-body Hamiltonian. It is shown that by using ˜v 14, all properties of cold nuclear matter can be correctly reproduced if TBF is used in RLOCV framework. The energy and proton abundance of BSM are calculated for a wide range of baryon number densities, which are of interest in astrophysics. It is also shown that by adding RC or TBF to our calculations, the maximum proton abundance is pushed toward lower densities. Furthermore, the particle number densities decrease by including RC and increase when TBF is added to the interactions. The opposite behaviors for the role TBF and RC on saturation properties of nuclear matter as well as proton number densities of nuclear β-stable matter are found. It is also shown that the effects of three-body forces are much larger than those of relativistic corrections.
