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

30 pages, 8 figures. v2: Minor corrections and references added. Conclusions unchanged. v3: Version published in PRD

References in corpus (17)

• The Universal Rotation Curve of Spiral Galaxies. II The Dark Matter Distribution out to the Virial Radius
• Dark energy and dark matter as curvature effects
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Non-Newtonian behavior in weak field general relativity for extended rotating sources
• Kinetic Theory of Collisionless Self-Gravitating Gases: Post-Newtonian Polytropes
• An Infinite Family of Generalized Kalnajs Disks
• General Relativity Resolves Galactic Rotation Without Exotic Dark Matter
• An Infinite Family of Self-consistent Models for Axisymmetric Flat Galaxies
• Two-integral distribution functions for axisymmetric systems
• Chaotic and regular motion around generalized Kalnajs discs
• Comment on ``General Relativity Resolves Galactic Rotation Without Exotic Dark Matter'' by F.I. Cooperstock & S. Tieu
• Charged Annular Disks and Reissner-Nordström Type Black Holes from Extremal Dust
• Fractional Derivative Approach to the Self-gravitation Equation
• Singular disk of matter in the Cooperstock-Tieu galaxy model
• Fokker-Planck-Rosenbluth-Type Equations for Self-gravitating Systems in 1PN Approximation
• General Relativistic Galaxy Rotation Curves: Implications for Dark Matter Distribution
• Velocity Curves for Stars in Disk Galaxies: A case for Nearly Newtonian Dynamics

Cited by in corpus (4)

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• Vertical stability of circular orbits in relativistic razor-thin disks
• On the rotation curves for axially symmetric disk solutions of the Vlasov-Poisson system
• Post-Newtonian Hamiltonian dynamics: applications to stationary spacetimes and statistical mechanics