Stellar structure model in the post-Newtonian approximation

In this work the influence of the post-Newtonian corrections to the equations of stellar structure is analysed. 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-Endem equations in the Newtonian and post-Newtonian theories are determined and the physical quantities for the $\mathit{\text{Sun}}$, for the white dwarf $\mathit{\text{Sirius}}\mathit{\text{B}}$ and for neutron stars with masses $M\simeq 1.4M_{\odot },1.8M_{\odot }$ and $2.0M_{\odot }$ are calculated. It is shown that the post-Newtonian corrections to the fields of mass density, pressure and temperature are negligible for the $\mathit{\text{Sun}}$ and $\mathit{\text{Sirius}}\mathit{\text{B}}$, but for stars with strong fields the differences become important. For the neutron stars analysed 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.