论文标题
革命表面上的测量：虫洞应用
Geodesy on surfaces of revolution: A wormhole application
论文作者
论文摘要
我们概述了一个一般程序，以在二维（2D）革命表面上遵守的一阶微分方程融入或嵌入普通的三维（3D）欧几里得空间中。我们用应用程序应用于Morris和Thorne（MT）引入的虫洞模型的应用，该过程提供了“可分布的时空”几何形状的原型情况。我们获得了根据椭圆形积分和功能表达的测量轨道的分析溶液，这些轨道在质量上与我们先前报道的Schwarzschild几何形状的副代阵代副代词相似，但更基本。两种大地测量学相应地出现。常规的测量学的转折点大于“喉咙”半径。因此，它们仍然局限于MT虫洞的一半。奇异的大地测量学通过喉咙漏斗，并连接MT虫洞的两半，也许提供了“快速的史诗间旅行”的可能性。我们提供了MT虫洞上两种大地轨道的数值插图。
We outline a general procedure to derive first-order differential equations obeyed by geodesic orbits over two-dimensional (2D) surfaces of revolution immersed or embedded in ordinary three-dimensional (3D) Euclidean space. We illustrate that procedure with an application to a wormhole model introduced by Morris and Thorne (MT), which provides a prototypical case of a `splittable space-time' geometry. We obtain analytic solutions for geodesic orbits expressed in terms of elliptic integrals and functions, which are qualitatively similar to, but even more fundamental than, those that we previously reported for Flamm's paraboloid of Schwarzschild geometry. Two kinds of geodesics correspondingly emerge. Regular geodesics have turning points larger than the `throat' radius. Thus, they remain confined to one half of the MT wormhole. Singular geodesics funnel through the throat and connect both halves of the MT wormhole, perhaps providing a possibility of `rapid inter-stellar travel.' We provide numerical illustrations of both kinds of geodesic orbits on the MT wormhole.
