A collision operator for field-mediated interactions in general relativistic kinetic theory
Abstract
Abstract We develop a Hamiltonian framework for general relativistic kinetic theory on the cotangent bundle T ∗ M of a Lorentzian (pseudo–Riemannian) manifold. Starting from the geodesic Hamiltonian H , we derive a Landau-type collision operator for self-gravitating particles undergoing binary interactions mediated by an arbitrary potential energy V , and couple the resulting kinetic stress–energy to the Einstein field equations to obtain the Landau–Einstein system. In the presence of a coordinate-time Killing symmetry we find a family of stationary states of the form f ∝ γ exp [ − β ( H + Φ ) ] ζ ( p 0 ) , where Φ is the mean field, γ = d t / d τ , β is an inverse-temperature parameter, and ζ encodes symmetry-induced degeneracy.
Fields of Study & Subjects
Cosmology and Gravitation Theories
Relativity and Gravitational Theory
Gas Dynamics and Kinetic Theory
Publication details
- Journal / source
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Volume
- 43
- Issue
- 4
- Pages
- 045003–045003
- Publication date
- 3 February 2026
- Language
- EN