Boundary conditions and the entropy bound

Details Boundary conditions and the entropy bound Boundary conditions and the entropy bound

2000-09-29

arxiv.org/abs/gr-qc/0009103v3

Phys.Rev. D63 (2001) 044002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, latex, v2: typos corrected, to appear in Phys.Rev.D

Scientific paper

10.1103/PhysRevD.63.044002

The entropy-to-energy bound is examined for a quantum scalar field confined to a cavity and satisfying Robin condition on the boundary of the cavity. It is found that near certain points in the space of the parameter defining the boundary condition the lowest eigenfrequency (while non-zero) becomes arbitrarily small. Estimating, according to Bekenstein and Schiffer, the ratio $S/E$ by the $\zeta$-function, $(24\zeta (4))^{1/4}$, we compute $\zeta (4)$ explicitly and find that it is not bounded near those points that signals violation of the bound. We interpret our results as imposing certain constraints on the value of the boundary interaction and estimate the forbidden region in the parameter space of the boundary conditions.

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