New bounds for the area of MOTS and generalized ultra-massive spacetimes

Abstract

Bounds for the area of general closed marginally trapped surfaces (MTSs) are presented. They do not require any stability condition, and are determined by a constant that depends on a particular component of the Einstein tensor on the surface and another constant that governs the (in)stability of the MTS. When stability is imposed, the area bounds are refined. These bounds are realized in spacetimes exhibiting interesting generic properties: they possess marginally trapped tubes foliated by marginally trapped topological spheres containing a distinguished round sphere $\bar S$ with constant Gaussian curvature that saturates the area bound. This distinguished surface separates two distinct regions of the marginally trapped tubes: a dynamical horizon and a timelike membrane. The particular case where there is a positive cosmological constant leads to the well-known universal bound $4π/ Λ$ for spatially stable MTSs, and to the recently introduced `ultra-massive spacetimes'. These spacetimes are more extreme than black holes, as there is no event horizon and the entire exterior region undergoes unavoidable collapse. In this paper similar behaviour is found for non-positive $Λ$ if the energy-momentum content is powerful enough. The results may have implications for binary mergers and on accreting very compact objects.