A dynamically transversely trapping surface (DTTS) is a newly born concept of an extension of a photon sphere that appropriately represents a strong gravity region and has close analogy with a trapped surface. We study formation of a marginally DTTS in time-symmetric, conformally flat initial data with two black holes, with a spindle-shaped source, and with a ring-shaped source, and clarify that $\mathcal{C}\lesssim 6\pi GM$ well describes the condition for the DTTS formation, where $\mathcal{C}$ is the circumference and $M$ is the mass of the system. This indicates that an understanding analogous to the hoop conjecture for the horizon formation is possible. Exploring the ring system further, we find configurations where a marginally DTTS with the torus topology forms inside a marginally DTTS with the spherical topology, without being hidden by an apparent horizon. There also exist configurations where a marginally trapped surface with the torus topology forms inside a marginally trapped surface with the spherical topology, showing a further similarity between DTTSs and trapped surfaces.

中文翻译：

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动态横向俘获面的形成和拉伸箍猜想

动态横向捕获表面 (DTTS) 是光子球扩展的新概念，它恰当地代表了一个强重力区域，并且与捕获表面非常相似。我们研究了时间对称、共形平坦初始数据中边缘 DTTS 的形成，其中包含两个黑洞、一个纺锤形源和一个环形源，并阐明 $\mathcal{C}\lesssim 6\pi GM$ 很好地描述了 DTTS 形成的条件，其中 $\mathcal{C}$ 是周长，$M$ 是系统的质量。这表明类似于对地平线形成的箍猜想的理解是可能的。进一步探索环形系统，我们发现在具有球面拓扑的边缘 DTTS 内形成具有环面拓扑的边缘 DTTS 的配置，不会被明显的地平线所掩盖。还存在这样的配置，其中具有环面拓扑的边缘捕获表面在具有球形拓扑的边缘捕获表面内形成，显示出 DTTS 和捕获表面之间的进一步相似性。