We present an invariant characterization of black holes in the Szekeres spacetime with positive cosmological constant. In the formation of the black holes, we locate geometric horizons, and show that they coincide with the more traditional apparent horizons in the Szekeres models. We also define an invariant approach for detecting shell crossings. It is shown that shell crossing regions in the Szekeres models can be contained within the geometric horizons for situations where no naked singularities form, allowing for the study of astrophysical models that are inhomogeneous and with a cosmological constant. A measure of inhomogeneity through the dipole functions in the Szekeres models is used to compute shell crossing surfaces along particular directions in the spacetime. An example of the method applied to the axially symmetric collapse of a quasispherical dust is given, motivated by previous work on primordial black hole formation. Future extensions and generalizations of this work are also discussed.

我们提出了具有正宇宙学常数的 Szekeres 时空中黑洞的不变特征。在黑洞的形成过程中，我们定位了几何视界，并表明它们与 Szekeres 模型中更传统的视视界一致。我们还定义了一种用于检测壳交叉的不变方法。结果表明，在没有裸奇点形成的情况下，Szekeres 模型中的壳层交叉区域可以包含在几何视界内，从而可以研究不均匀且具有宇宙学常数的天体物理模型。通过 Szekeres 模型中的偶极子函数测量不均匀性，用于计算时空中沿特定方向的壳交叉表面。受先前关于原始黑洞形成的工作的启发，给出了应用于准球形尘埃的轴对称坍缩的方法示例。还讨论了这项工作的未来扩展和概括。