Mann R B, Chak P
Department of Physics, University of Waterloo, Waterloo, Ontario, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Feb;65(2 Pt 2):026128. doi: 10.1103/PhysRevE.65.026128. Epub 2002 Jan 22.
We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of N particles coupled to lineal gravity and can be considered as a model of N relativistically interacting sheets of uniform mass. The partition function and one-particle distribution functions are computed to leading order in 1/c where c is the speed of light; as c --> infinity results for the nonrelativistic one-dimensional self-gravitating system are recovered. We find that relativistic effects generally cause both position and momentum distribution functions to become more sharply peaked, and that the temperature of a relativistic gas is smaller than its nonrelativistic counterpart at the same fixed energy. We consider the large-N limit of our results and compare this to the nonrelativistic case.
我们考虑一个广义相对论的一维自引力系统的统计力学。该系统由与线性引力耦合的N个粒子组成，可被视为N个具有均匀质量的相对论性相互作用薄片的模型。计算了在1/c（其中c为光速）下的配分函数和单粒子分布函数的主导阶；当c趋于无穷大时，恢复了非相对论一维自引力系统的结果。我们发现相对论效应通常会使位置和动量分布函数的峰值变得更尖锐，并且在相同的固定能量下，相对论气体的温度低于其非相对论对应物。我们考虑结果的大N极限，并将其与非相对论情况进行比较。
