Collective classical motion on hyperbolic spacetimes of any dimensions

TL;DR

This paper derives the geodesic equations and Boltzmann models for particles on de Sitter and anti-de Sitter spacetimes of any dimension, providing explicit distribution functions in terms of conserved quantities.

Contribution

It introduces a general framework for analyzing kinetic theory on hyperbolic spacetimes, including explicit Boltzmann equations and distribution functions for these geometries.

Findings

Derived geodesic equations on hyperbolic spacetimes.

Formulated Boltzmann equations in terms of conserved quantities.

Provided explicit distribution functions for kinetic models.

Abstract

The geodesics equations on de Sitter and anti-de Sitter spacetimes of any dimensions, are the starting point for deriving the general form of the Boltzmann equation in terms of conserved quantities. The simple equation for the non-equilibrium Marle and Anderson-Witting models are derived and the distributions of the Boltzmann-Marle model on these manifolds are written down first in terms of conserved quantities and then as functions of canonical variables.