发表机构
University of Bonn; Oriel College, University of Oxford（波恩大学; 牛津大学奥里尔学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文探讨广义相对论中闵可夫斯基时空的特权地位，提出$\delta$-平坦性判据并推广，证明其无自由参数地唯一区分闵可夫斯基时空，而较弱变体$\delta$-MSS选出最大对称时空族。
AI 中文摘要
是什么（如果有的话）使得闵可夫斯基时空在广义相对论中成为一种特权的局部参考几何？最近Weatherall和Fletcher的工作认为：没有。作为回应，我提出了一个“$\delta$-平坦性”判据，该判据将管状邻域内的潮汐加速度大小限制在$\delta$以内，并证明了闵可夫斯基时空唯一地达到该界限。在此，我探讨$\delta$-平坦性如何推广，并区分两种扩展类型。参考度量推广将物理潮汐加速度与由另一度量构造的参考潮汐力项进行比较。洛伦兹符号阻碍了所有参考度量与物理度量不共享光锥的比较。判据修改则仅从物理几何本身构建判据。这类修改的空间很广，我聚焦于最接近$\delta$-平坦性的那些，即限制潮汐加速度与非零目标的偏差。最小候选者，我称之为$\delta$-MSS，具有一个奇异极限，通过Schur定理选出最大对称时空（闵可夫斯基、德西特、反德西特）。一个受限变体，将$g$与其自身的共形重标度进行比较，要么退化为$\delta$-MSS，要么无法选出唯一几何。主要结果是，$\delta$-平坦性以无自由参数的方式区分闵可夫斯基时空。$\delta$-MSS，一个较弱的变体，以外部提供的标量为代价选出最大对称族。
英文摘要
What, if anything, makes Minkowski spacetime a privileged local reference geometry in General Relativity? Recent work by \cite{WeatherallFletcher} argues: nothing. In response, I proposed a criterion of ``$δ$-flatness'', which bounds the magnitude of tidal acceleration within a tubular neighborhood by $δ$, and showed that Minkowski uniquely saturates the bound. Here I ask how $δ$-flatness generalises, and distinguish two kinds of extension. Reference-metric generalisations compare physical tidal acceleration with a reference tidal-force term constructed from another metric. Lorentzian signature obstructs every such comparison in which the reference fails to share the lightcones of the physical metric. Criterion modifications instead build the criterion from the physical geometry alone. The space of such modifications is wide, and I focus on those closest to $δ$-flatness, where one bounds the deviation of tidal acceleration from a non-zero target. The minimal candidate, which I call $δ$-MSS, has a singular limit that picks out the maximally symmetric spacetimes (Minkowski, de Sitter, Anti-de Sitter) via Schur's theorem. A restricted variant, which compares $g$ with a conformal rescaling of itself, either collapses to $δ$-MSS or fails to pick out a unique geometry. The chief result is that $δ$-flatness distinguishes Minkowski with no free parameter. $δ$-MSS, a weaker variant, picks out the maximally symmetric family at the cost of an externally supplied scalar.
Comments19 pages
