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

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.

preprint2022arXivOpen access
Gilberto M. Kremer
gr-qc
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Gilberto M. Kremer

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