Equation of State of a Self-gravitating Fluid with Rotating Particles

Abstract

The equation of state for a system interacting via a gravitational potential, is obtained. This potential is found in the context of general relativity from the Kerr metric, when considering the so-called weak-field limit and perfoming an angular average to have a potential with spherical symmetry. The resulting potential is naturally regular and bounded by effect of angular momentum. Microcanonical and canonical ensembles are studied, calculating their thermodynamic potential, finding the corresponding equation of state. Afterwards both ensembles are compared in the diluted regime showing explicitly their equivalence.

Perturbation theory for very long-range potentials

“…In the context of general relativity, within the weak-field limit methodology, an angular averaged potential due to the interaction between two identical spherical rotating bodies was proposed [21]. This interaction potential for hard-core spheres is given by U * (x) ≡ U(x)/ | ǫ min |, where:…”

“…As an illustrative example, we have choosed the gravitational potential due to the interaction between two identical spherical rotating bodies (ETS potential), obtained by Escamilla et al [21]. More interesting models in the context of molecular liquids, could be, for instance, the Coulomb interactions.…”