Entropy bounds in terms of the w parameter

Details Entropy bounds in terms of the w parameter Entropy bounds in terms of the w parameter

2011-09-13

arxiv.org/abs/1109.2710v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

V1: 14 pages. V2: One reference added. V3: This version accepted for publication in JHEP

Scientific paper

In a pair of recent articles [PRL 105 (2010) 041302 - arXiv:1005.1132; JHEP 1103 (2011) 056 - arXiv:1012.2867] two of the current authors have developed an entropy bound for equilibrium uncollapsed matter using only classical general relativity, basic thermodynamics, and the Unruh effect. An odd feature of that bound, S <= A/2, was that the proportionality constant, 1/2, was weaker than that expected from black hole thermodynamics, 1/4. In the current article we strengthen the previous results by obtaining a bound involving the (suitably averaged) w parameter. Simple causality arguments restrict this averaged parameter to be <= 1. When equality holds, the entropy bound saturates at the value expected based on black hole thermodynamics. We also add some clarifying comments regarding the (net) positivity of the chemical potential. Overall, we find that even in the absence of any black hole region, we can nevertheless get arbitrarily close to the Bekenstein entropy.

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