Prepared for the proceedings of the IX Mexican School of the Gravitation and Mathematical Physics Division of the Mexican Physical Society, 30 pages, 1 figure
We present a brief introduction to the relativistic kinetic theory of gases with emphasis on the underlying geometric and Hamiltonian structure of the theory. Our formalism starts with a discussion on the tangent bundle of a Lorentzian manifold of arbitrary dimension. Next, we introduce the Poincare one-form on this bundle, from which the symplectic form and a volume form are constructed. Then, we define an appropriate Hamiltonian on the bundle which, together with the symplectic form yields the Liouville vector field. The corresponding flow, when projected onto the base manifold, generates geodesic motion. Whenever the flow is restricted to energy surfaces corresponding to a negative value of the Hamiltonian, its projection describes a family of future-directed timelike geodesics. A collisionless gas is described by a distribution function on such an energy surface, satisfying the Liouville equation. Fibre integrals of the distribution function determine the particle current density and the stress-energy tensor. We show that the stress-energy tensor satisfies the familiar energy conditions and that both the current and stress-energy tensor are divergence-free.
Our discussion also includes the generalization to charged gases, a summary of the Einstein-Maxwell-Vlasov system in any dimensions, as well as a brief introduction to the general relativistic Boltzmann equation for a simple gas.
Non-relativistic transport from frame-indifferent kinetic theory
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Institute of Theoretical Physics, Wroclaw University of Science and Technology（弗罗茨瓦夫科技大学理论物理研究所）
The complete relativistic kinetic model of violation of symmetry in isotopic expanding plasma and production of baryons in hot Universe. I. Exact model
The complete relativistic kinetic model of violation of symmetry in isotopic expanding plasma and production of baryons in hot Universe. II. Numerical model: X-boson distribution function
The energy-momentum tensor in relativistic kinetic theory: the role of the center of mass velocity in the transport equations for multicomponent mixtures
Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relativistic and relativistic case - A simple proof for finite extension
Heat flux in the presence of a gravitational field in a simple dilute fluid: an approach based in general relativistic kinetic theory to first order in the gradients
Richard C.托尔曼分析了温度梯度与平衡状态下的引力场之间的关系。在2012年，托尔曼\textquoteright定律被推广到一个简单的稀释相对论性流体的非平衡情况。在这种情况下的结果，通过引入引力通过分子加速度，耦合的度量系数和状态变量的梯度的热通量。本文通过对玻尔兹曼方程中的分子加速度\textquoteright进行\textquotedblright{}抑制，证明了引力场驱动热流。这个过程对应于通过测地线的粒子运动的描述，其中假设史瓦西度规的牛顿极限。这种效应在非相对论区域消失，这可以通过直接计算相应的极限得到证明。
Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics
在本文中，我们研究的动力学理论的多粒子天体物理系统施加轴对称性和扩展我们以前的分析在物理Rev. D 83，123007（2011）。从描述无碰撞自引力气体的牛顿模型出发，我们发展了一个框架，系统地包括对一般静止系统的物质分布和引力势的第一次广义相对论修正。然后，我们使用我们的方法来获得特定的解决方案的情况下，摩根和摩根磁盘。得到的模型是完全解析的，对应于后牛顿的经典的概括。我们探讨了一些属性的模型，以估计后牛顿修正的重要性，我们发现，与预期相反，主要的修改出现远离星系核心。作为这项研究的副产品，我们推导出了张量维里定理的修正版本。对于定常系统，我们得到了与牛顿理论相同的结果。然而，对于依赖于时间的背景，我们发现有一个额外的部分，有助于惯性张量的变化。
