Post-Newtonian Jeans Equation for Stationary and Spherically Symmetrical Self-Gravitating Systems

Abstract

The post-Newtonian Jeans equation for stationary self-gravitating systems is derived from the post-Newtonian Boltzmann equation in spherical coordinates. The Jeans equation is coupled with the three Poisson equations from the post-Newtonian theory. The Poisson equations are functions of the energy-momentum tensor components which are determined from the post-Newtonian Maxwell–Jüttner distribution function. As an application, the effect of a central massive black hole on the velocity dispersion profile of the host galaxy is investigated and the influence of the post-Newtonian corrections are determined.

Keywords

• post-Newtonian theory
• Boltzmann equation
• Jeans equation
• self-gravitating systems