Collective classical motion on hyperbolic spacetimes of any dimensions

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.

13 pages, no figures

References in corpus (8)

• Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
• Special Relativity in the 21${}^{\mathrm{st}}$ century
• Conservation laws and scattering for de Sitter classical particles
• Rest frames and relativistic effects on de Sitter spacetimes
• de Sitter geodesics
• de Sitter relativity in central charts
• Anti-de Sitter relativity
• Physical meaning of the conserved quantities on anti-de Sitter geodesics