Newtonian gravity in d dimensions

Details Newtonian gravity in d dimensions Newtonian gravity in d dimensions

2006-12-04

arxiv.org/abs/astro-ph/0612086v1

Comptes Rendus Physique 7 (2006) 331

Astronomy and Astrophysics

Astrophysics

Scientific paper

10.1016/j.crhy.2006.01.005

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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