Axially Symmetric Post-Newtonian Stellar Systems

TL;DR

This paper develops an analytical method to create self-consistent, axially symmetric stellar disk models in the first post-Newtonian approximation, revealing significant relativistic effects on galaxy rotation curves.

Contribution

It introduces a fully analytical approach to extend classical stellar disk models into the 1PN regime using the Hunter method.

Findings

1PN corrections significantly affect rotation curves.

Relativistic mass correction is negligible for typical galaxy models.

Models are analytical and generalize classical solutions.

Abstract

We introduce a method to obtain self-consistent, axially symmetric, thin disklike stellar models in the first post-Newtonian (1PN) approximation. The models obtained are fully analytical and corresponds to the post-Newtonian generalizations of classical ones. By introducing in the field equations provided by the 1PN approximation a known distribution function (DF) corresponding to a Newtonian model, two fundamental equations determining the 1PN corrections are obtained, which are solved using the Hunter method. The rotation curves of the 1PN-corrected models differs from the classical ones and, for the generalized Kalnajs discs, the 1PN corrections are clearly appreciable with values of the mass and radius of a typical galaxy. On the other hand, the relativistic mass correction can be ignored for all models.