发表机构
University of California, Berkeley; Stanford University; Princeton University（加州大学伯克利分校; 斯坦福大学; 普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构造了渐近平直时空零无穷远截断面处的可观测量代数，分析了含/不含黑洞时空的代数类型，为黑洞代数构建了正则化并证明了相关量子场的两项技术结果。
AI 中文摘要
我们构造了与渐近平直时空中零无穷远的一个截断面相关联的可观测量代数。未来零无穷远的尖锐截断面对应的邦迪质量并非良定义的量子算子：即使在推迟时间中做涂抹，其涨落仍会发散。我们转而引入有限半径、经时间涂抹的邦迪质量版本，并将该算子附加到该截断面任意小渐近邻域内的物质与引力子可观测量中。我们分别分析了含黑洞与不含黑洞的时空，发现两种情形下均存在满足非平凡嵌套关系的III₁型冯·诺依曼代数。在闵氏时空中，所得代数可重构该截断面对应的类空楔；在稳态黑洞时空中，它可重构由该截断面与黑洞分叉面界定的区域，提供了纠缠楔的渐近平直类比。当截断面移至过去无穷远时，不含黑洞的时空对应I∞型代数，含黑洞的时空对应II∞型代数。对于推迟时间有限截断面处的代数，我们构造了黑洞代数的II∞型正则化，其重正化冯·诺依曼熵与广义熵一致。附录中，我们证明了关于史瓦西时空中量子场的两项技术结果：这些量子场在无穷远处渐近于闵氏真空，一是无界类空分离区域的拆分性质，二是构造了忠实、正规且半有限的Hartle-Hawking权，其模流为史瓦西时间演化。
英文摘要
We construct an algebra of observables associated to a cut of null infinity in asymptotically flat spacetimes. The Bondi mass associated with a sharp cut of future null infinity is not a well-defined quantum operator: its fluctuations diverge even after smearing in retarded time. We instead introduce a finite-radius, time-smeared version of the Bondi mass and adjoin this operator to the matter and graviton observables in an arbitrarily small asymptotic neighborhood of the cut. We separately analyze spacetimes with and without black holes and find, in both cases, Type III$_1$ von Neumann algebras that satisfy non-trivial nesting relations. In Minkowski spacetime, the resulting algebra reconstructs the spacelike wedge associated with the cut. In a stationary black hole spacetime, it reconstructs the region bounded by the cut and the black hole bifurcation surface, providing an asymptotically flat analogue of an entanglement wedge. In the limit as the cut is moved to past infinity, we recover a Type I$_{\infty}$ algebra for spacetimes without black holes and a Type II$_{\infty}$ algebra for black hole spacetimes. For algebras at finite cuts of retarded time, we construct a Type II$_\infty$ regularization of the black hole algebra whose renormalized von Neumann entropy agrees with the generalized entropy. In appendices, we prove two technical results about quantum fields, in a Schwarzschild spacetime, that asymptote to the Minkowski vacuum at infinity: a split property for unbounded, spacelike separated regions and the construction of a faithful, normal, and semifinite Hartle-Hawking weight whose modular flow is Schwarzschild time evolution.
Comments49 pages + appendices, 10 figures
