G. Cognola et L. Vanzo, BOSE-EINSTEIN CONDENSATION OF SCALAR FIELDS ON HYPERBOLIC MANIFOLDS, Physical review. D. Particles and fields, 47(10), 1993, pp. 4575-4580
The problem of Bose-Einstein condensation for a relativistic ideal gas
on an ultrastatic (3+1)-dimensional manifold with a hyperbolic spatia
l part is analyzed in some detail. The critical temperature is evaluat
ed and its dependence on curvature is pointed out. Complete expansions
for the thermodynamic potential are given for the cases of both low a
nd high temperature.