We present \textbf{warpax}, an open-source, GPU-accelerated Python toolkit for observer-robust energy condition analysis of warp drive spacetimes. Instead of sampling a finite set of observer directions, \textbf{warpax} performs continuous, gradient-based optimization on the timelike observer manifold, parameterized by rapidity and boost direction and informed by the Hawking-Ellis classification. At Type~I stress-energy points, which account for more than $96%$ of grid points across tested metrics, energy-condition satisfaction is determined \emph{exactly} through an algebraic eigenvalue check, independent of observer search or rapidity caps. At non-Type~I points, the optimizer provides rapidity-capped diagnostics. Stress-energy tensors are computed from the ADM metric via forward-mode automatic differentiation, eliminating finite-difference error. Geodesic integration with tidal-force and blueshift analysis is included. We evaluate five warp drive metrics (Alcubierre, Lentz, Van~Den~Broeck, Nat'ario, Rodal) and a warp shell metric as a numerical stress test. For the Rodal metric, Eulerian-frame analysis misses violations at more than $28%$ of grid points for the dominant energy condition and more than $15%$ for the weak energy condition. Even when the violation region is correctly identified, observer optimization shows that violation severity can be orders of magnitude larger; for example, for Alcubierre the weak energy condition reaches $\sim 9\times 10^{4}$ at rapidity cap $ζ_{\max}=5$, scaling as $e^{2ζ_{\max}}$, where the cap is an analysis hyperparameter. These results show that single-frame evaluation can substantially underestimate both the spatial extent and magnitude of energy-condition violations. \textbf{warpax} is available at https://github.com/anindex/warpax.
翻译:我们提出了**warpax**——一个开源的、GPU加速的Python工具包,用于曲速驱动时空的观测者鲁棒性能量条件分析。与对有限观测方向进行采样的传统方法不同,**warpax**在类时观测者流形上执行基于梯度的连续优化,该流形由快度和助推方向参数化,并依据霍金-埃利斯分类进行构建。在I型应力-能量点(占测试度规中超过$96\%$的网格点)处,能量条件的满足情况通过代数特征值检查得以**精确**判定,无需依赖观测者搜索或快度上限。在非I型点处,优化器提供带快度上限的诊断结果。应力-能量张量通过前向模式自动微分从ADM度规计算得出,消除了有限差分误差。工具包还包含测地线积分以及潮汐力和蓝移分析功能。我们评估了五种曲速驱动度规(Alcubierre、Lentz、Van Den Broeck、Nat'ario、Rodal)和一种曲速壳度规作为数值应力测试。对于Rodal度规,欧拉框架分析在超过$28\%$的网格点上漏报了主导能量条件的违反,在超过$15\%$的网格点上漏报了弱能量条件的违反。即使在正确识别违反区域的情况下,观测者优化显示违反严重程度可能高出数个数量级;例如,对于Alcubierre度规,在快度上限$ζ_{\max}=5$时弱能量条件达到$\sim 9\times 10^{4}$,其缩放规律为$e^{2ζ_{\max}}$,其中上限为分析超参数。这些结果表明,单框架评估可能严重低估能量条件违反的空间范围和幅度。**warpax**可在https://github.com/anindex/warpax获取。