Toroidal trapped surfaces and isoperimetric inequalities

Understand

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.