论文标题

部分可观测时空混沌系统的无模型预测

The Spacetime Geometry of Fixed-Area States in Gravitational Systems

论文作者

Dong, Xi, Marolf, Donald, Rath, Pratik, Tajdini, Amirhossein, Wang, Zhencheng

论文摘要

事实证明,固定区域状态的概念对最近的量子重力研究有用,尤其是与重力全息相关的研究。我们在本文中探讨了此类固定区域固有的洛伦兹签名时空几何形状。这与以前的治疗方法形成鲜明对比,这些治疗集中在欧几里得 - 签名的马鞍上,用于准备这样的状态的路径积分。我们分析了固定区域几何形状的一般特征,并构建了明确的例子。时空指标在实际时期是真实的,没有圆锥形的奇异性。凭借足够的对称性,经典指标实际上是平滑的,尽管更普遍的曲率具有沿固定区域表面正交发射的无量子的幂律差异。虽然我们认为这种分歧在经典层面上并非有问题,但固定区域状态的量子场具有更强的分歧。因此,在量子水平上,我们期望固定区域只有在适当涂抹固定区域表面时才能明确定义。

The concept of fixed-area states has proven useful for recent studies of quantum gravity, especially in connection with gravitational holography. We explore the Lorentz-signature spacetime geometry intrinsic to such fixed-area states in this paper. This contrasts with previous treatments which focused instead on Euclidean-signature saddles for path integrals that prepare such states. We analyze general features of fixed-area state geometries and construct explicit examples. The spacetime metrics are real at real times and have no conical singularities. With enough symmetry the classical metrics are in fact smooth, though more generally their curvatures feature power-law divergences along null congruences launched orthogonally from the fixed-area surface. While we argue that such divergences are not problematic at the classical level, quantum fields in fixed-area states feature stronger divergences. At the quantum level we thus expect fixed-area states to be well-defined only when the fixed-area surface is appropriately smeared.

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