Thermodynamics of ideal boson and fermion gases in the static Taub universe

Abstract

Some thermodynamic quantities of nonrelativistic ideal boson and fermion gases in the static Taub universe are derived to first order in a small anisotropy parameter d measuring the deformation from the spherical Einstein universe. They are used to investigate the problem of how the curvature anisotropy affects the thermodynamic behaviors of an ideal gas. It is found that, when the universe is in the oblate configuration (i.e., d≳0), the effect of curvature anisotropy is to increase the number of the fraction in the Bose–Einstein condensation and to decrease the fermion distribution function at low temperature. When the universe is in the prolate configuration (i.e., d<0), the effects of curvature anisotropy on the thermodynamic quantities is contrary to that in the oblate configuration. The density matrix of a two particle system is evaluated and it is used to define the ‘‘statistical interparticle potential’’ as an attempt to give a ‘‘statistical interpretation’’ about the found thermodynamic behaviors. It is found that when the universe is in the oblate (prolate) configuration the curvature anisotropy will enhance (reduce) both the ‘‘statistic attraction’’ among the bosons and ‘‘statistical repulsion’’ among the fermions. It is expected that such a behavior will also be shown in the relativistic system.