Stellar structure model in the post-Newtonian approximation

TL;DR

This paper investigates how post-Newtonian corrections affect stellar structure models, showing negligible effects for Sun-like stars but significant differences for neutron stars, especially in central pressure and temperature.

Contribution

It derives and solves the post-Newtonian Lane-Emden equation for different stellar types, highlighting the importance of relativistic corrections in dense stars.

Findings

Post-Newtonian corrections are negligible for Sun and Sirius B.

Significant increases in central pressure and temperature for neutron stars.

Central mass density decreases slightly in neutron stars with post-Newtonian corrections.

Abstract

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 \textit{Sun}, for the white dwarf \textit{Sirius B} and for neutron stars with masses $M\simeq1.4M_\odot, 1.8M_\odot$ 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 \textit{Sun} and \textit{Sirius 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.