病理性Misner型时空的因果分类
Causal classification of pathological Misner-type spacetimes
AI总结：
本文通过分析三种因果违反时空模型，证明其在覆盖空间和因果正则区域内的等因果性，为分类提供了严谨框架。
摘要：
我们研究了三种因果违反时空：Misner空间（包括Kip Thorne的“移动墙”模型）、伪Schwarzschild时空以及新引入的伪Reissner-Nordström时空。尽管它们的物理起源不同——从平坦真空解到黑洞型真空解再到非真空模型，需要奇异物质——它们都具有共同的扭曲积结构，二维圆柱形基度量和基本因果特征，如Cauchy和时间线 horizon、非因果区域以及类地轨行为。基于2016年提出的猜想，我们证明了这三个模型在其全域覆盖空间和合适因果正则区域内的配对等因果性。证明是建设性的，提供了覆盖空间上的显式因果双射，并识别了一个具体的deck-等价性准则，用于降级到紧凑时空：如果等价度满足|k|=1，则模型是全局等因果的，否则如果|k|>1或等价性失效，则在紧凑模型之间最多存在单向因果关系。这些结果为这些时空提供了严谨的因果分类，将它们纳入统一的Misner型家族，并为扩展到其他因果违反解的分类提供了框架。
英文摘要：
We investigate three causality-violating spacetimes: Misner space (including Kip Thorne's "moving wall" model), the pseudo-Schwarzschild spacetime, and a new model introduced here, the pseudo-Reissner-Nordström spacetime. Despite their different physical origins -- ranging from a flat vacuum solution to a black-hole-type vacuum solution to a non-vacuum model requiring exotic matter -- all three share a common warped-product structure, $2$-dimensional cylindrical base metrics of Eddington-Finkelstein type, and fundamental causal features such as Cauchy and chronology horizons, acausal regions, and analogous geodesic behaviour. Building on a conjecture first proposed in 2016, we present a formal proof that the three models are pairwise isocausal on their universal covers and on suitable causally regular regions of their compactified forms. The proof is constructive, providing explicit causal bijections on the covers and identifying a concrete deck-equivariance criterion governing descent to the compactified spacetimes: if the equivariance degree satisfies $|k|=1$ the models are globally isocausal, whereas if $|k|>1$ or equivariance fails, then at most a one-way causal relation holds between the compactified models. These results supply a rigorous causal classification linking these spacetimes, placing them within a unified Misner-type family and providing a framework for extending the classification to other causality-violating solutions.
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