Toroidal trapped surfaces and isoperimetric inequalities

Abstract

We analytically construct 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.

4 pages

References in corpus (2)

• Topological Appearance of Event Horizon: What Is the Topology of the Event Horizon That We Can See?
• Initial Data for General Relativity Containing a Marginally Outer Trapped Torus

Cited by in corpus (9)

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• Symmetry and instability of marginally outer trapped surfaces
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• Exotic marginally outer trapped surfaces in rotating spacetimes of any dimension
• Self-gravitating perfect-fluid tori around black holes: Bifurcations, ergoregions, and geometrical properties
• Toroidal magnetic fields in self-gravitating disks around black holes
• Marginally Outer Trapped Tori in Black Hole Spacetimes
• Analytical solution of Brill waves
• Hayward Quasilocal Energy of Tori