Abstrakt
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 Lemaitre 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 Lemaitre-Tolman-Bondi spacetime. We then study the Szekeres-Szafron spacetime with no symmetries, particularly its subfamily with beta(,z) not equal 0, and we find conditions on the horizon existence in a general spacetime as well as in certain special cases.