Entropy Bound for the TM Electromagnetic Field in the Half Einstein Universe

Abstract

An explicit calculation is given of the entropy/energy ratio for the TM modes of the electromagnetic field in the half Einstein universe. This geometry provides a mathematically convenient and physically instructive example of how the electromagnetic and thermodynamic quantities behave as a function of the nondimensional parameter δ=1/2πaT, a being the scale factor and T the temperature. On physical grounds (related to the relaxation time), it is the case of small δ's that is pertinent to thermodynamics. We find that as long as δis small, the entropy/energy ratio behaves in the same way as for the TE modes. The entropy is thus bounded. The present kind of formalism makes it convenient to study also the influence from frequency dispersion. We discuss an example where a sharp cutoff dispersion relation can in principle truncate the electromagnetic oscillations in the Einstein cavity such that only the lowest mode survives.

14 pages, no figures, discussion extended. To appear in Int. J. Mod. Phys. D

References in corpus (10)

• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• General Logarithmic Corrections to Black Hole Entropy
• The Casimir effect: Recent controversies and progress
• Non-linear electrodynamics and the acceleration of the universe
• Does the Transverse Electric Zero Mode Contribute to the Casimir Effect for a Metal?
• Entropy bounds, monotonicity properties and scaling in CFTs
• Entropy Bounds in $R\times S^3$ Geometries
• Electromagnetic Casimir energy with extra dimensions
• p-form spectra and Casimir energies on spherical tesselations

Cited by in corpus (1)

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