外熵= Bartnik-Bray内质量，引力蚂蚁猜想
Outer entropy = Bartnik-Bray inner mass, and the gravitational ant conjecture
摘要：
熵和能量被发现与我们对量子引力的探索密切相关。我们指出了最近提出的外熵，一个粗粒度的熵定义的紧凑的时空域的动机的全息对偶，和Bartnik-Bray准局部质量之间的一个有趣的连接在数学界早就知道。在这两种情况下，人们都在寻找一个给定的封闭的、连通的、类空的、余维为2的边界的最佳时空填充。我们表明，对于一个外部最小化的平均凸曲面，Bartnik-Bray内部质量完全匹配的不可约质量对应的外部熵。等价性意味着由外熵导出的面积定律在数学上等价于准局部质量的单调性。它也在熵和引力能之间产生了新的界限，这自然地给出了沃尔的蚂蚁猜想的引力对应物。我们还观察到，平等可以实现共形流的度量，这是结构上类似的Ceyhan-Faulkner证明的蚂蚁猜想。我们计算小球体极限的外熵，它是成比例的体应力张量，因为人们会期望一个准局部质量。最后，我们讨论了在半经典背景下考虑量子物质的一些含义。
英文摘要：
Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime fill-in of a given closed, connected, spacelike, codimension-two boundary. We show that for an outer-minimizing mean-convex surface, the Bartnik-Bray inner mass matches exactly with the irreducible mass corresponding to the outer entropy. The equivalence implies that the area laws derived from the outer entropy are mathematically equivalent as the monotonicity property of the quasilocal mass. It also gives rise to new bounds between entropy and the gravitational energy, which naturally gives the gravitational counterpart to Wall's ant conjecture. We also observe that the equality can be achieved in a conformal flow of metrics, which is structurally similar to the Ceyhan-Faulkner proof of the ant conjecture. We compute the small sphere limit of the outer entropy and it is proportional to the bulk stress tensor as one would expect for a quasilocal mass. Lastly, we discuss some implications of taking quantum matter into consideration in the semiclassical setting.
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