高斯曲率与整体效应：引力Aharonov-Bohm效应再论
Gaussian Curvature and Global effects : gravitational Aharonov-Bohm effect revisited
摘要：
利用高斯-博内公式，在静态时空的渐近平坦区域中，在由曲线包围的2-曲面上的高斯曲率的积分被发现是Ford和Vilenkin在线性化区域中的Aharonov-Bohm效应的引力模拟的度量。利用时空分解的1+3公式，我们研究了静止时空中完全爱因斯坦场方程的相同效应。将我们的方法应用于尘埃的静态管状和圆柱形分布，我们不仅恢复了它们的结果，而且还获得了一个额外的项，该项被解释为代表经典版本的Colella-Overhauser-Werner效应（COW实验）。
英文摘要：
Using the Gauss-Bonnet formula, integral of the Gaussian curvature over a 2-surface enclosed by a curve in the asymptotically flat region of a static spacetime was found to be a measure of a gravitational analogue of Aharonov-Bohm effect by Ford and Vilenkin in the linearized regime. Employing the 1+3 formulation of spacetime decomposition we study the same effect in the context of full Einstein field equations for stationary spacetimes. Applying our approach to static tube-like and cylindrical distributions of dust not only we recover their result but also obtain an extra term which is interpreted to be representing the classical version of the Colella-Overhauser-Werner effect (the COW experiment).
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