Newtonian gravity in d dimensions
arXiv:astro-ph/0612086 · doi:10.1016/j.crhy.2006.01.005
Abstract
We study the influence of the dimension of space on the thermodynamics of the classical and quantum self-gravitating gas. We consider Hamiltonian systems of self-gravitating particles described by the microcanonical ensemble and self-gravitating Brownian particles described by the canonical ensemble. We present a gallery of caloric curves in different dimensions of space and discuss the nature of phase transitions as a function of the dimension d. We also provide the general form of the Virial theorem in d dimensions and discuss the particularity of the dimension d=4 for Hamiltonian systems and the dimension d=2 for Brownian systems.
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- Self-gravitating Brownian particles in two dimensions: the case of N=2 particles
- Dynamical origin of non-thermal states in galactic filaments
- Collisional relaxation of two-dimensional self-gravitating systems
- Gravitational phase transitions with an exclusion constraint in position space
- Virial theorem for rotating self-gravitating Brownian particles and two-dimensional point vortices
- Self-gravitating clusters of Fermi-Dirac gas with planar, cylindrical, or spherical symmetry: evolution of density profiles with temperature
- Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: gaseous density profiles and onset of condensation