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Newtonian gravity in d dimensions

Pierre-Henri Chavanis
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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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Pierre-Henri Chavanis. 2006-12-04. Newtonian gravity in d dimensions. https://doi.org/10.1016/j.crhy.2006.01.005

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