In this work the influence of the post-Newtonian corrections to the equations of stellar structure are analyzed. The post-Newtonian Lane–Emden equation follows from the corresponding momentum density balance equation. From a polytropic equation of state the solutions of the Lane–Emden equations in the Newtonian and post-Newtonian theories are determined and the physical quantities for the Sun, the white dwarf Sirius B and neutron stars with masses M ≃ 1.4 M, 1.8 M and 2.0 M are calculated. It is shown that the post-Newtonian corrections to the fields of mass density, pressure and temperature are negligible for the Sun and Sirius B, but for stars with strong fields the differences become important. For the neutron stars analyzed here the central pressure and the central temperature which follow from the post-Newtonian Lane–Emden equation are about fifty to sixty percent greater than those of the Newtonian theory and the central mass density is about three to four percent smaller.
stars: neutron – stars: fundamental parameters – hydrodynamics
It accepts original submissions from all over the world and is internationally published and distributed by IOP