Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics

TL;DR

This paper extends the kinetic theory of collisionless self-gravitating gases to include first-order relativistic corrections, providing analytical models for galactic disks and analyzing the significance of these corrections in different regions.

Contribution

It develops a systematic framework for incorporating relativistic effects into kinetic models of galactic systems and derives analytical solutions for specific disk models.

Findings

Relativistic corrections are more significant far from galaxy centers.

Derived a relativistic version of the tensor virial theorem.

Models show that post-Newtonian effects can influence galaxy dynamics.

Abstract

In this paper we study the kinetic theory of many-particle astrophysical systems imposing axial symmetry and extending our previous analysis in Phys. Rev. D 83, 123007 (2011). Starting from a Newtonian model describing a collisionless self-gravitating gas, we develop a framework to include systematically the first general relativistic corrections to the matter distribution and gravitational potentials for general stationary systems. Then, we use our method to obtain particular solutions for the case of the Morgan & Morgan disks. The models obtained are fully analytical and correspond to the post-Newtonian generalizations of classical ones. We explore some properties of the models in order to estimate the importance of post-Newtonian corrections and we find that, contrary to the expectations, the main modifications appear far from the galaxy cores. As a by-product of this investigation we derive the corrected version of the tensor virial theorem. For stationary systems we recover the same result as in the Newtonian theory. However, for time dependent backgrounds we find that there is an extra piece that contributes to the variation of the inertia tensor.