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Equilibrium states of gravitational systems

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Abstract

We formulate the equilibrium correlation functions for local observables of an assembly of non-relativistic, neutral gravitating fermions in the limit where the number of particles becomes infinite, and in a scaling where the region θ, to which they are confined, remains fixed. We show that these correlation functions correspond, in the limit concerned, to states on the discrete tensor product\(\mathop \otimes \limits_{x \in \Omega } A_x \), where the\(A_x 's\) are copies of the gauge invariantC*-algebra\(A\) of the CAR overL 2(R 3). The equilibrium states themselves are then given by\(\mathop \otimes \limits_{x \in \Omega } \bar \omega _{\varrho 0(x)} \), where\(\bar \omega _\varrho \), is the Gibbs state on\(A\) for an infinitely extended ideal Fermi gas at density ϱ, and where ϱ0 is the normalised density function that minimises the Thomas-Fermi functional, obtained in [2], governing the equilibrium thermodynamics of the system.

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Communicated by H. Araki

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Narnhofer, H., Sewell, G.L. Equilibrium states of gravitational systems. Commun.Math. Phys. 71, 1–28 (1980). https://doi.org/10.1007/BF01230083

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