Relativistic ab initio calculations for static and rotating neutron stars

Neutron stars are extraordinary astrophysical objects with densities close to and even very far above these in atomic nuclei. Their structure and dynamic observables are governed by the equation of state (EoS). Due to difficulties in both theory and experiments, there exist still big uncertainties on the EoS for neutron stars. From the realistic nucleon–nucleon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> interactions fitted to the experimental <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:mi>N</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:math> scattering data, the ab initio calculations based on exact many-body theory are expected to provide a reliable EoS for neutron stars. In this mini review, the relativistic Brueckner–Hartree–Fock theory within the full Dirac space will be introduced, the technical for relieving the angle-averaging approximations will be addressed, and its description for neutron star properties will be introduced.