全金属测地线透镜作为静态球对称引力场的模拟电磁模型
Fully metallic geodesic lenses as analog electromagnetic models of static and spherically symmetric gravitational fields
AI总结：
本文提出用全金属空气填充测地线波导模拟静态球对称引力场，通过Plebanski形式体系将时空度规编码为折射率分布，并成功复现Schwarzschild黑洞和Morris-Thorne虫洞的零测地线，仿真平均相对误差小于4%。
摘要：
我们证明，一种全金属且空气填充的测地线波导可以用作静态球对称引力场的模拟电磁模型。通过遵循Plebanski形式体系，首先将上述类型的时空度规编码到一个平坦时空区域的电磁特性中，其形式为各向同性且沿径向变化的折射率分布。然后，采用一个三维、空气填充且轴对称的波导，该波导由两个等间距的弯曲金属表面构成。其形状经过专门设计，使得微波辐射的横向电磁光束在该波导内所遵循的有效路径，等效于在上述折射介质中发生的零测地线。该策略避免了对折射介质的需求，尽管它只能在不变平面上重现时空度规。利用所提出的方法，设计了两个引力的模拟电磁模型，以重现Schwarzschild黑洞和Morris-Thorne虫洞的度规。全波仿真结果表明，一维高斯光束忠实地沿着一条与广义相对论零测地线完全等效的路径传播，平均相对误差在4%以内。
英文摘要：
We demonstrate that a fully metallic and air-filled geodesic waveguide can be employed as an analog electromagnetic model of a static and spherically symmetric gravitational field. By following the Plebanski formalism, a space-time metric of the aforementioned type is firstly encoded into the electromagnetic properties of a flat space-time region in the form of an isotropic and radially varying refractive index distribution. Then, a three-dimensional, air-filled, and axially symmetric waveguide, composed of two equally spaced and curved metallic surfaces, is employed. Its shape is tailored such that the effective paths, followed by transverse electromagnetic beams of microwave radiation within this waveguide, result equivalent to null-geodesics taking place in the aforementioned refractive medium. This strategy avoids the need for a refractive medium, although it only allows to reproduce the space-time metric on the invariant plane. Two analog electromagnetic models of gravity, using the proposed approach, are designed to reproduce the metric of both a Schwarzschild black hole and a Morris-Thorne wormhole. The results from full-wave simulations demonstrate that a one-dimensional Gaussian beam faithfully follows a path completely equivalent to general relativistic null geodesics with a mean relative error within 4%.
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