Saturating the holographic entropy bound
Saturating the holographic entropy bound
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饱和全息熵界
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Stefan Leichenauer
中科院分区：
文献类型：
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作者：
R. Bousso;Ben Freivogel;Stefan Leichenauer
The covariant entropy bound states that the entropy, $S$, of matter on a light sheet cannot exceed a quarter of its initial area, $A$, in Planck units. The gravitational entropy of black holes saturates this inequality. The entropy of matter systems, however, falls short of saturating the bound in known examples. This puzzling gap has led to speculation that a much stronger bound, $Sensuremath{lesssim}{A}^{3/4}$, may hold true. In this note, we exhibit light sheets whose entropy exceeds ${A}^{3/4}$ by arbitrarily large factors. In open Friedmann-Robertson-Walker universes, such light sheets contain the entropy visible in the sky; in the limit of early curvature domination, the covariant bound can be saturated but not violated. As a corollary, we find that the maximum observable matter and radiation entropy in universes with positive (negative) cosmological constant is of order ${ensuremath{Lambda}}^{ensuremath{-}1}$ (${ensuremath{Lambda}}^{ensuremath{-}2}$), and not $|ensuremath{Lambda}{|}^{ensuremath{-}3/4}$ as had hitherto been believed. Our results strengthen the evidence for the covariant entropy bound, while showing that the stronger bound $Sensuremath{lesssim}{A}^{3/4}$ is not universally valid. We conjecture that the stronger bound does hold for static, weakly gravitating systems.
The covariant entropy bound states that the entropy, $S$, of matter on a light sheet cannot exceed a quarter of its initial area, $A$, in Planck units. The gravitational entropy of black holes saturates this inequality. The entropy of matter systems, however, falls short of saturating the bound in known examples. This puzzling gap has led to speculation that a much stronger bound, $Sensuremath{lesssim}{A}^{3/4}$, may hold true. In this note, we exhibit light sheets whose entropy exceeds ${A}^{3/4}$ by arbitrarily large factors. In open Friedmann-Robertson-Walker universes, such light sheets contain the entropy visible in the sky; in the limit of early curvature domination, the covariant bound can be saturated but not violated. As a corollary, we find that the maximum observable matter and radiation entropy in universes with positive (negative) cosmological constant is of order ${ensuremath{Lambda}}^{ensuremath{-}1}$ (${ensuremath{Lambda}}^{ensuremath{-}2}$), and not $|ensuremath{Lambda}{|}^{ensuremath{-}3/4}$ as had hitherto been believed. Our results strengthen the evidence for the covariant entropy bound, while showing that the stronger bound $Sensuremath{lesssim}{A}^{3/4}$ is not universally valid. We conjecture that the stronger bound does hold for static, weakly gravitating systems.