Quasilocal horizons in inhomogeneous cosmological models

Abstract

We investigate quasilocal horizons in inhomogeneous cosmological models, specifically concentrating on the notion of a trapping horizon defined by Hayward as a hypersurface foliated by marginally trapped surfaces. We calculate and analyse these quasilocally defined horizons in two dynamical spacetimes used as inhomogeneous cosmological models with perfect fluid source of non-zero pressure. In the spherically symmetric Lemaître spacetime we discover that the horizons (future and past) are both null hypersurfaces provided that the Misner–Sharp mass is constant along the horizons. Under the same assumption we come to the conclusion that the matter on the horizons is of special character—a perfect fluid with negative pressure. We also find out that they have locally the same geometry as the horizons in the Lemaître–Tolman–Bondi spacetime. We then study the Szekeres–Szafron spacetime with no symmetries, particularly its subfamily with , and we find conditions on the horizon existence in a general spacetime as well as in certain special cases.