标题： 高能闭合弦的碰撞：环状视界形成 显示英文标题

标题： Collision of high-energy closed strings: Formation of a ring-like apparent horizon

摘要： 我们研究在$D$维广义相对论框架下两个高能闭合弦的碰撞。 高能闭合弦的模型被引入为由半径为$R$的环形源产生的{/it pp}波。 在碰撞的瞬间，假设两条弦的位置精确重合。 在此设置中，我们研究两种类型的似是而非视界（AHs）的形成：拓扑为$S^{D-2}$的AH（黑洞AH）和拓扑为$S^1/times S^{D-3}$的AH（黑洞环AH）。 这两种AHs通过数值求解，且在环半径$R$的条件下明确了这两种AHs形成的条件。 具体而言，我们证明当$R$足够大时，黑洞环AH会形成。 在更一般的情况下，简要讨论了碰撞参数和入射弦相对取向的影响。 显示英文摘要

摘要： We study collisions of two high-energy closed strings in the framework of $D$-dimensional general relativity. The model of a high-energy closed string is introduced as a {/it pp}-wave generated by a ring-shaped source with the radius $R$. At the instant of the collision, the positions of two strings are assumed to coincide precisely. In this setup, we study the formation of two kinds of apparent horizons (AHs): the AH of topology $S^{D-2}$ (the black hole AH) and the AH of topology $S^1/times S^{D-3}$ (the black ring AH). These two AHs are solved numerically and the conditions for the formation of the two AHs are clarified in terms of the ring radius $R$. Specifically, we demonstrate that the black ring AH forms for sufficiently large $R$. The effects of an impact parameter and the relative orientation of incoming strings in more general cases are briefly discussed.