Gravitational positive energy theorems from information inequalities
Gravitational positive energy theorems from information inequalities
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DOI：
10.1093/ptep/ptw139
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发表时间：
2016-05
影响因子：
3.5
通讯作者：
Nima Lashkari;Jennifer Lin;H. Ooguri;Bogdan Stoica;M. Raamsdonk
中科院分区：
文献类型：
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作者：
Nima Lashkari;Jennifer Lin;H. Ooguri;Bogdan Stoica;M. Raamsdonk
在本文中，我们认为，经典的渐近反德西特时空中出现的爱因斯坦引力耦合到物质的一致的紫外线完成的状态必须满足一个无限的家庭的正能量条件。对于边界时空的每个球形空间区域B，我们可以将B和具有与B相同边界的体极值表面B之间的体空间区域B关联起来。我们表明，存在一个自然的概念，引力能的每一个这样的区域是非负的，不增加，因为一个使该地区更小。结果如下从确定这个引力能与量子相对熵在相关的对偶共形场论状态。引力能的正性和单调性是由相对熵的正性和单调性所隐含的，这在所有量子系统中普遍成立。
In this paper we argue that classical asymptotically anti-de Sitter spacetimes that arise as states in consistent ultraviolet completions of Einstein gravity coupled to matter must satisfy an infinite family of positive energy conditions. To each ball-shaped spatial region B of the boundary spacetime we can associate a bulk spatial region Σ_B between B and the bulk extremal surface B with the same boundary as B. We show that there exists a natural notion of a gravitational energy for every such region that is non-negative, and non-increasing as one makes the region smaller. The results follow from identifying this gravitational energy with a quantum relative entropy in the associated dual conformal field theory state. The positivity and monotonicity properties of the gravitational energy are implied by the positivity and monotonicity of relative entropy, which holds universally in all quantum systems.