A Collision Operator for Field-Mediated Interactions in General Relativistic Kinetic Theory
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914337833091072 |
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| author | Sato, Naoki |
| author_facet | Sato, Naoki |
| contents | We develop a Hamiltonian framework for general relativistic kinetic theory on the cotangent bundle $T^{\ast}M$ 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 $f \propto γ\exp[-β(H+Φ)]ζ(p_0)$, where $Φ$ is the mean field, $γ=dt/dτ$, $β$ is an inverse-temperature parameter, and $ζ$ encodes symmetry-induced degeneracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19405 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Collision Operator for Field-Mediated Interactions in General Relativistic Kinetic Theory Sato, Naoki General Relativity and Quantum Cosmology We develop a Hamiltonian framework for general relativistic kinetic theory on the cotangent bundle $T^{\ast}M$ 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 $f \propto γ\exp[-β(H+Φ)]ζ(p_0)$, where $Φ$ is the mean field, $γ=dt/dτ$, $β$ is an inverse-temperature parameter, and $ζ$ encodes symmetry-induced degeneracy. |
| title | A Collision Operator for Field-Mediated Interactions in General Relativistic Kinetic Theory |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2411.19405 |