精度依赖的正规邻域中的物理学
Physics in precision-dependent normal neighborhoods
摘要：
我们介绍了一个程序来确定正常的邻居在任何时空的大小和形状和它们的依赖于任意观察者进行测量的精度。作为一个例子，我们考虑在黎曼和费米正常坐标的史瓦西几何，并确定在事件视界附近的正常邻域的大小和形状。根据观察者的不同，正常邻域会延伸到事件视界，甚至更远的地方，进入黑洞内部。结果表明，事件视界上的正常邻域所支持的因果结构与广义相对论是一致的。特别地，到达事件视界上方的正常邻域不存在史瓦西坐标奇点。此外，我们引入了一种新的变体的正常坐标，我们称之为费米正常坐标围绕一个点，统一的黎曼和费米正常坐标的功能，并分析其邻域。
英文摘要：
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.
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