We numerically study the algebraic properties of the Weyl tensor through the merger of two non-spinning black holes (BHs). We are particularly interested in the conjecture that for such a vacuum spacetime, which is zeroth-order algebraically general, a geometric horizon (GH), on which the spacetime is algebraically special and which is identified by the vanishing of a complex scalar invariant (), characterizes a smooth foliation independent surface (horizon) associated with the BH. In the first simulation we investigate the level-0 sets of (since ) in the head-on collision of two unequal mass BHs. In the second simulation we shall investigate the level-ɛ sets of through a quasi-circular merger of two non-spinning, equal mass BHs. The numerical results, as displayed in the figures presented, provide evidence that a (unique) smooth GH can be identified throughout all stages of the binary BH merger.

我们通过两个非自旋黑洞 (BH) 的合并来数值研究外尔张量的代数性质。我们对这样一个猜想特别感兴趣，即对于这样的真空时空，它是零阶代数通用的，几何视界（GH），其上的时空在代数上是特殊的，并且通过复标量不变量（）的消失来识别，表征与 BH 相关的光滑叶理独立表面（地平线）。在第一个模拟中，我们研究了两个质量不等的 BH 正面碰撞中的 0 级集（因为）。在第二个模拟中，我们将研究水平ɛ集通过两个非旋转的等质量 BH 的准圆形合并。如图所示，数值结果提供了证据，证明在二元 BH 合并的所有阶段都可以识别（独特的）平滑 GH。