arXiv 1806.028042018-06-22hep-thastro-ph.HEgr-qc

高维时空中的全息熵束缚：一如既往的强大

The holographic entropy bound in higher-dimensional spacetimes: As strong as ever

Shahar Hod

备注：: 5 pages
发表信息：: Phys. Rev. D 97, 126012 (2018)
DOI：: 10.1103/PhysRevD.97.126012

摘要：

著名的全像熵限（holographic entropy bound）认为，在自洽量子引力理论的框架内，一个物理系统的最大熵（信息）含量是由其外接面积的四分之一给出的：$S\leq S_{\text{max}}={\cal A}/4{\ell^2_P}$（这里$\ell_P$是普朗克长度）。一个有趣的可能反例，这个基本的熵界，其中涉及{ \it homogenous}弱自引力约束的热场在高维时空，已提出了近十年前。有趣的是，在本文中，我们将证明，这个组成的物理系统，乍一看似乎违反了全息熵界，实际上符合熵面积不等式$S\leq {\cal A}/4{\ell^2_P}$。特别是，我们将明确表明，封闭的热场的均匀性设置系统的熵含量的上限。因此，目前的分析解决了在高维时空中的封闭的热场约束的全息熵的明显违反。

英文摘要：

The celebrated holographic entropy bound asserts that, within the framework of a self-consistent quantum theory of gravity, the maximal entropy (information) content of a physical system is given by one quarter of its circumscribing area: $S\leq S_{\text{max}}={\cal A}/4{\ell^2_P}$ (here $\ell_P$ is the Planck length). An intriguing possible counter-example to this fundamental entropy bound, which involves {\it homogenous} weakly self-gravitating confined thermal fields in higher-dimensional spacetimes, has been proposed almost a decade ago. Interestingly, in the present paper we shall prove that this composed physical system, which at first sight seems to violate the holographic entropy bound, actually conforms to the entropy-area inequality $S\leq {\cal A}/4{\ell^2_P}$. In particular, we shall explicitly show that the homogeneity property of the confined thermal fields sets an upper bound on the entropy content of the system. The present analysis therefore resolves the apparent violation of the holographic entropy bound by confined thermal fields in higher-dimensional spacetimes.

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