Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems

Details Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems

2001-01-27

arxiv.org/abs/gr-qc/0101106v1

Phys.Rev. E65 (2002) 026128

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

latex, 60 pages, 22 figures

Scientific paper

10.1103/PhysRevE.65.026128

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 distitrubion functions are computed to leading order in $1/c$ where $c$ is the speed of light; as $c\to\infty$ results for the non-relativistic 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 non-relativistic counterpart at the same fixed energy. We consider the large-N limit of our results and compare this to the non-relativistic case.

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