Examples of toroidal trapped surfaces

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Written by Patryk Mach

This is a joint work with Janusz Karkowski, Edward Malec, Niall O Murchadha and Naqing Xie on trapped toroidal surfaces. We construct (analytically) an infinite number of trapped toroids in spherically symmetric Cauchy hypersurfaces of the Einstein equations. We focus on initial data which represent "constant density stars" momentarily at rest. There exists an infinite number of constant mean curvature tori, but we also deal with more general configurations. The marginally trapped toroids have been found analytically and numerically; they are unstable. The topologically toroidal trapped surfaces appear in a finite region surrounded by the Schwarzschild horizon. The corresponding paper is posted on arXiv as arXiv:1701.02861