Gravitational phase transitions in a one-dimensional spherical system

Area of Science:

• Astrophysics and Gravitational Physics
• Statistical Mechanics
• Computational Physics

Background:

• Investigating gravitational systems with phase transitions is crucial for understanding cosmic structure formation.
• Ensemble theory provides a framework for analyzing thermodynamic properties of many-body systems.
• Mean-field theory offers a simplified approach to complex gravitational interactions.

Purpose of the Study:

• To investigate gravitational phase transitions in systems of concentric, spherical mass shells.
• To analyze the behavior of these transitions across microcanonical, canonical, and grand canonical ensembles.
• To compare theoretical predictions from mean-field theory with results from dynamical simulations.

Main Methods:

• Theoretical analysis using mean-field theory for different statistical ensembles.
• Dynamical simulations to model the behavior of mass shells under self- and mutual gravitation.
• Examination of finite-size scaling effects and temporal/positional correlations.

Main Results:

• Mean-field theory predicts transitions between uniform and centrally concentrated states in microcanonical and canonical ensembles, supported by simulations.
• In the grand canonical ensemble, mean-field theory predicts no transition, with the uniform state being always stable, also supported by simulations.
• Dynamical simulations revealed vanishing temporal and positional correlations in the mean-field limit.

Conclusions:

• Gravitational phase transition behavior is ensemble-dependent in spherical mass shell systems.
• Mean-field theory provides a useful, albeit simplified, framework for understanding these transitions.
• Dynamical simulations are essential for capturing phenomena beyond the mean-field approximation, such as correlations.