Ultra-massive spacetimes

Abstract

A positive cosmological constant $\Lambda >0$ sets an upper limit for the area of marginally future-trapped surfaces enclosing a black hole (BH). Does this mean that the mass of the BH cannot increase beyond the corresponding limit? I analyze some simple spherically symmetric models where regions within a dynamical horizon keep gaining mass-energy so that eventually the $\Lambda$ limit is surpassed. This shows that the black hole proper transmutes into a collapsing universe, and no observers will ever reach infinity, which dematerializes together with the event horizon and the ‘cosmological horizon’. The region containing the dynamical horizon cannot be causally influenced by the vast majority of the spacetime, its past being just a finite portion of the total, spatially infinite, spacetime. Thereby, a new type of horizon arises, but now relative to past null infinity: the boundary of the past of all marginally trapped spheres, which contains in particular one with the maximum area $4\pi /\Lambda$. The singularity is universal and extends mostly outside the collapsing matter. The resulting spacetime models turn out to be inextendible and globally hyperbolic. It is remarkable that they cannot exist if $\Lambda$ vanishes. Given the accepted value of $\Lambda$ deduced from cosmological observations, such ultra-massive objects will need to contain a substantial portion of the total present mass of the observable universe.