论文标题
与精确依赖的正常社区中的物理学
Physics in precision-dependent normal neighborhoods
论文作者
论文摘要
我们介绍了一项程序，以确定任何空间中正常邻域的大小和形状及其对任意观察者执行的测量精度的依赖。例如，我们考虑Riemann和Fermi正常坐标中的Schwarzschild几何形状，并确定事件范围附近正常邻居的大小和形状。根据观察者的不同，正常社区延伸到事件范围，甚至延伸到黑洞内部。结果表明，事件范围内正常社区支持的因果结构与一般相对论一致。特别是，到达事件视野的正常社区没有Schwarzschild坐标的奇异性。此外，我们引入了一种新的正常坐标变体，我们称之为费米正常坐标，在一个点附近，统一了Riemann和Fermi正常坐标的特征，并分析了其社区。
We introduce a procedure to determine the size and shape of normal neighborhoods in any spacetimes and their dependence on the precision of the measurements performed by arbitrary observers. As an example, we consider the Schwarzschild geometry in Riemann and Fermi normal coordinates and determine the size and shape of normal neighborhoods in the vicinity of the event horizon. Depending on the observers, normal neighborhoods extend to the event horizon and even beyond into the black hole interior. It is shown that the causal structure supported by normal neighborhoods across an event horizon is consistent with general relativity. In particular, normal neighborhoods reaching over an event horizon are void of the Schwarzschild coordinate singularity. In addition, we introduce a new variant of normal coordinates which we call Fermi normal coordinates around a point, unifying features of Riemann and Fermi normal coordinates, and analyze their neighborhoods.
