论文标题
外部熵= Bartnik-Bray内部质量和重力蚂蚁猜想
Outer entropy = Bartnik-Bray inner mass, and the gravitational ant conjecture
论文作者
论文摘要
发现熵和能量与我们对量子重力的追求紧密相关。我们指出了最近提出的外部熵之间的有趣联系，这是一个由全息二元性动机的紧凑时空域定义的粗粒熵与在数学社区中已知的长期已知的Bartnik-Bray Quasilocal质量。在这两种情况下，都寻求给定的封闭，连接，空间般的codimension-two边界的最佳时空填充。我们表明，对于外部最小化均应符号表面，bartnik-bray内质量与与外熵相对应的不可约质量完全匹配。等效性意味着从外部熵得出的面积定律在数学上是准质量的单调性特性。它还引起了熵和重力之间的新界限，这自然会使引力与墙的蚂蚁猜想相对。我们还观察到，可以在指标的共形流中实现平等，这在结构上与蚂蚁猜想的锡汉 - 福克纳证据相似。我们计算外部熵的小球体极限，它与散装应力张量成正比，因为人们对准局部质量的期望会期望。最后，我们讨论了在半经典环境中考虑量子问题的一些含义。
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.
