1202.5970 (Andrzej Krasiński et al.)

Apparent horizons in the quasi-spherical Szekeres models    [PDF]

Andrzej Krasiński, Krzysztof Bolejko

The notion of an apparent horizon (AH) in a collapsing object can be carried over from the Lema\^{\i}tre -- Tolman (L--T) to the quasi-spherical Szekeres models in three ways: 1. Literally by the definition -- the AH is the envelope of the region, in which every bundle of null geodesics has negative expansion scalar. 2. As the locus, at which null lines that are as nearly radial as possible are turned toward decreasing areal radius $R$. These lines are in general nongeodesic. The name "absolute apparent horizon" (AAH) is proposed for this locus. 3. As the envelope of a region, where null \textit{geodesics} are turned toward decreasing $R$. The name "light collapse region" (LCR) is proposed for this region (which is 3-dimensional in every space of constant $t$); its boundary coincides with the AAH. The AH and AAH coincide in the L--T models. In the quasi-spherical Szekeres models, the AH is different from (but not disjoint with) the AAH. Properties of AAH and LCR are investigated, and the relations between the AAH and the AH are illustrated with diagrams using an explicit example of a Szekeres metric. It turns out that an observer who is already within the AH is, for some time, not yet within the AAH. Nevertheless, no light signal can be sent inside out through the AH. The analogue of AAH for massive particles is also considered.

View original: http://arxiv.org/abs/1202.5970