Entropy Bounds in $R\times S^3$ Geometries

Details Entropy Bounds in $R\times S^3$ Geometries Entropy Bounds in $R\times S^3$ Geometries

2002-02-07

arxiv.org/abs/hep-th/0202048v4

Annals Phys.302:120-141,2002

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, no figures, REVTeX4. Revised paper contains minor corrections and clarifications

Scientific paper

10.1006/aphy.2002.6317

Exact calculations are given for the Casimir energy for various fields in $R\times S^3$ geometry. The Green's function method naturally gives a result in a form convenient in the high-temperature limit, while the statistical mechanical approach gives a form convenient for low temperatures. The equivalence of these two representations is demonstrated. Some discrepancies with previous work are noted. In no case, even for ${\cal N}=4$ SUSY, is the ratio of entropy to energy found to be bounded. This deviation, however, occurs for low temperature, where the equilibrium approach may not be relevant. The same methods are used to calculate the energy and free energy for the TE modes in a half-Einstein universe bounded by a perfectly conducting 2-sphere.

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