Kinetic Theory of Collisionless Self-Gravitating Gases: Post-Newtonian Polytropes

Abstract

In this paper we study the kinetic theory of many-particle astrophysical systems and we present a consistent version of the collisionless Boltzmann equation in the 1PN approximation. We argue that the equation presented by Rezania and Sobouti in A&A 354 1110 (2000) is not the correct expression to describe the evolution of a collisionless self-gravitating gas. One of the reasons that account for the previous statement is that the energy of a free-falling test particle, obeying the 1PN equations of motion for static gravitational fields, is not a static solution of the mentioned equation. The same statement holds for the angular momentum, in the case of spherical systems. We provide the necessary corrections and obtain an equation that is consistent with the corresponding equations of motion and the 1PN conserved quantities. We suggest some potential relevance for the study of high density astrophysical systems and as an application we construct the corrected version of the post-Newtonian polytropes.

23 pages, 24 figures. Accepted for publication in PRD

References in corpus (3)

• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Fractional Derivative Approach to the Self-gravitation Equation
• Fokker-Planck-Rosenbluth-Type Equations for Self-gravitating Systems in 1PN Approximation

Cited by in corpus (12)

• Relativistic kinetic gases as direct sources of gravity
• Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics
• Post-Newtonian Kinetic Theory
• Plane wave analysis of the second post-Newtonian hydrodynamic equations
• Post-Newtonian Jeans Equation for Stationary and Spherically Symmetrical Self-Gravitating System
• Relaxation-Time Model for the Post-Newtonian Boltzmann Equation
• $q$-Equilibrium of Gas in Spacetime of Multi-horizon Black Holes
• Stellar structure model in the post-Newtonian approximation
• Post-Newtonian non-equilibrium kinetic theory
• Post-Newtonian Hamiltonian dynamics: applications to stationary spacetimes and statistical mechanics
• Jeans Instability from post-Newtonian Boltzmann equation
• A general relativistic kinetic theory approach to linear transport in generic hydrodynamic frame