2024/11/28 by Sato, Naoki
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2411.19405
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 ∝ γexp[-β(H+Φ)]ζ(p0), where Φ is the mean field, γ=dt/dτ, β is an inverse-temperature parameter, and ζ encodes symmetry-induced degeneracy.