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.

arXiv comment23 pages, 24 figures. Accepted for publication in PRD

References in corpus (6)

• Primordial Nucleosynthesis: Successes And Challenges
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Long-term Evolution of Stellar Self-Gravitating System away from the Thermal Equilibrium: connection with non-extensive statistics
• Fokker-Planck type equations for a simple gas and for a semi-relativistic Brownian motion from a relativistic kinetic theory
• Fractional Derivative Approach to the Self-gravitation Equation
• Fokker-Planck-Rosenbluth-Type Equations for Self-gravitating Systems in 1PN Approximation

Cited by in corpus (22)

• Jeans analysis of self-gravitating systems in f(R)-gravity
• On incorporating post-Newtonian effects in N-body dynamics
• Anisotropic Models for Globular Clusters, Galactic Bulges and Dark Halos
• Analytical families of 2-component anisotropic polytropes and their relativistic extensions
• Relativistic kinetic gases as direct sources of gravity
• Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics
• Self-gravitating systems of ideal gases in the 1PN approximation
• The Dark Matter distribution function and Halo Thermalization from the Eddington equation in Galaxies
• Post-Newtonian Kinetic Theory
• The double-power approach to spherically symmetric astrophysical systems
• Plane wave analysis of the second post-Newtonian hydrodynamic equations
• Post-Newtonian Jeans Equation for Stationary and Spherically Symmetrical Self-Gravitating System
• Self-Gravitating Relativistic Models of Fermions with Anisotropy and Cutoff Energy in their Distribution Function
• $q$-Equilibrium of Gas in Spacetime of Multi-horizon Black Holes
• Post-Newtonian non-equilibrium kinetic theory
• A core-halo pattern of entropy creation in gravitational collapse
• Relaxation-Time Model for the Post-Newtonian Boltzmann Equation
• Stellar structure model in the post-Newtonian approximation
• Asymmetric Velocity Distributions from Halo Density Profiles in the Eddington Approach
• Jeans Instability from post-Newtonian Boltzmann equation
• Post-Newtonian Hamiltonian dynamics: applications to stationary spacetimes and statistical mechanics
• A general relativistic kinetic theory approach to linear transport in generic hydrodynamic frame