Arising of trapped surfaces with non-trivial topology from colliding shock waves

Abstract

The lightlike limit of boosted black hole solutions with one angular momentum is considered for $D\ge 4$ dimensions. The boost is performed parallel to the angular momentum and the lightlike limit is done by means of perturbative expansions. We shown that for $D=4$ and $D>5$ the lightlike limit cannot be extended inside the ring singularity. Then, for $D=5$ we discuss the arising of trapped surfaces in the head-on collision. We find that, inside the validity of the perturbative analysis we do, a trapped surface with topology $\mathbb{R}\times {\mathbb{S}}_1\times {\mathbb{S}}_1$ seems to appear over the past light cone of the collision below a critical value $a_c$ of the Kerr parameter $a$.

23 pages, 2 figures

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