Static and rotating neutron stars in a relativistic formulation of all fundamental interactions and astrophysical applications

In the first part of our work, we formulated the equilibrium equa- tions for static neutron stars, taking into account strong, weak, elec- tromagnetic, and gravitational interactions within the framework of general relativity and relativistic nuclear mean field theory. We shown that the Tolman-Oppenheimer-Volkoff (TOV) equations are super- seded and the use of the Einstein-Maxwell-Thomas-Fermi (EMTF) sys- tem of equations is mandatory. The key points are the constancy of the general relativistic Fermi energies of particles, the “Klein potentials”, throughout the configuration, and the use of the global charge neutral- ity over the whole configuration as requested by the EMTF system of equations. The local charge neutrality is replaced due to its inconsis- tency with the equations of motions of the EMTF system of equations. The solution of EMTF leads to a new structure of the neutron stars: a positively charged core at supranuclear density, surrounded by an electron layer of thickness of the order of the electron screening scale, and at lower density, a neutral ordinary crust. Then, we introduced rotation on the new neutron stars model, fol- lowing the slow rotation approximation in the Hartle-Thorne formal- ism. Integrating the equations of equilibrium for different central den- sities and circular velocities, we have been able to compute mass M, polar Rp and equatorial Req radii , angular momentum J, eccentric- ity ǫ and quadrupole moment Q of the configurations. We accounted for the Keplerian mass-shedding limit and the axisymmetric secular instability. We computed the minimum mass for the globally neutral neutron stars, under which them result gravitationally unbound. No unbound configurations have been found for the locally neutral neutron stars, meaning that no minimum mass limit exist for this case. Afterward, we showed the inaccuracy of some analytic universal formulas, generally used in the literature, for the Keplerian sequence and for the moment of inertia of neutron stars. The values for the mo- ment of inertia I and the Keplerian rotational frequency fK, obtained through our model, have been compared and contrasted with such for- mulas. We analyzed the effect on the magnetic field of pulsars on respect to the case in which fiducial parameters are used. We showed that the magnetic field inferred from the magnetic-dipole formula can be overestimated up to one order of magnitude if fiducial parameters are adopted. We analyzed in particular the case of the high-magnetic field pulsar class. We found that the magnetic field of all the high- magnetic field pulsars can turn to be under-critical for appropriate values of the neutron star mass. We finally computed the range of neutron star masses for which the X-ray luminosity of these pulsars can be well explained via the loss of rotational energy and therefore they fall into the family of ordinary rotation powered pulsars.