Stellar structure model in the post-Newtonian approximation

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 $M\simeq 1.4M_{\odot },1.8M_{\odot }$ 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 \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.

8 pages, 3 figures

References in corpus (5)

• Helioseismology and Solar Abundances
• Kinetic Theory of Collisionless Self-Gravitating Gases: Post-Newtonian Polytropes
• Gravito-magnetic instabilities of Relativistic Magnetohydrodynamics
• Post-Newtonian Spherically Symmetrical Accretion
• Post-Newtonian Jeans Equation for Stationary and Spherically Symmetrical Self-Gravitating System