A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natário warp drives at a constant velocity. Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes, such as warp drives. Warp drives are the theoretical solutions to Einstein’s field equations that allow for the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter’s unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natário warp drive do not contain a wake or a constant curvature, indicating that these are unique features of the accelerating Natário warp drive.

中文翻译：

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Alcubierre和Natário经线驱动器的曲率不变量

应用了使用曲率不变式的过程来以恒定速度评估Alcubierre和Natário经纱驱动器的度量。曲率不变量与坐标基无关，因此绘制这些不变量将没有坐标映射失真。因此，它们为复杂的时空（例如翘曲驱动器）提供了新颖的视角。翘曲驱动是爱因斯坦场方程的理论解决方案，它允许比光速快（FTL）行驶。虽然他们的数学已经很好地建立了，但是这种时空的可视化还没有被探索。本文使用计算和绘制翘曲驱动曲率不变量的方法来揭示这些时空。速度的经向驱动参数 蒙皮深度和半径分别变化，然后绘制以查看每个参数对周围曲率的独特影响。对于每个翘曲驱动器，此研究均显示了安全的避风港以及形状函数如何形成翘曲气泡。恒速纳塔里奥经纱机的曲率图不包含尾迹或恒定曲率，这表明这些是加速纳塔里奥经纱机的独特功能。