2001/01/27 by Robert B. Mann, R. B. Mann, P. Chak
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Cosmology and Gravitation Theories #Distribution (mathematics) #Distribution function #Energy–momentum relation #Gravitation #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Partition function (quantum field theory) #Physics #Position (finance) #Quantum mechanics #Relativistic mechanics #Relativistic particle #Relativistic quantum chemistry #Statistical Mechanics and Entropy #Statistical mechanics #Theory of relativity #astro-ph #cond-mat.stat-mech #gr-qc
paper · pdf · doi:10.1103/physreve.65.026128
published as Phys.Rev. E65 (2002) 026128 · latex, 60 pages, 22 figures
arxiv created 2001/01/27 · openalex publication_date 2002/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.