Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems

Abstract

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.

latex, 60 pages, 22 figures

References in corpus (3)

• Exact Solutions to the Motion of Two Charged Particles in Lineal Gravity
• Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity
• Energy for N-Body Motion in Two Dimensional Gravity

Cited by in corpus (7)

• Chaos in a Relativistic 3-body Self-Gravitating System
• Cosmology in One Dimension: Fractal Geometry, Power Spectra and Correlation
• Chaos in an Exact Relativistic 3-body Self-Gravitating System
• 3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating System
• Dynamical N-body Equlibrium in Circular Dilaton Gravity
• One-Dimensional Relativistic Self-Gravitating Systems
• Dynamical Charged N-body Equilibrium in Circular Dilaton Gravity