http://arxiv.org/abs/1604.02003
In an earlier paper, it was shown that blueshifts generated in Lema\^{\i}tre — Tolman (L–T) models can account for sources of the gamma-ray bursts (GRBs). Sufficiently strong blueshifts are generated on radial rays emitted at such radial coordinates $r$ where the bang-time function $t_B(r)$ has $\dril {t_B} r \neq 0$. The aim of the present paper is to show that equally strong blueshifts can be generated in quasi-spherical Szekeres (QSS) models. It is shown that in an axially symmetric QSS model, infinite blueshift can appear only on axial rays, which intersect every space orthogonal to the dust flow on the symmetry axis. In an explicit such model it is numerically shown that if the ray is emitted from the Big Bang (BB) where $\dril {t_B} r \neq 0$, then indeed all observers see $z \approx -1$. Rays emitted shortly after the BB and running close to the symmetry axis will reach the observer with strong, albeit finite, blueshift. An additional (compared to an L–T model) free function allows one to increase the diameter of the blueshift-generating region and thereby to more efficiently account for the properties of the GRBs. The blueshift is generated around only two opposite directions, which should account for the hypothetical collimation of the GRBs. Then, in a toy QSS model that has no symmetry, it was shown by numerical calculations that two null lines exist such that rays in their vicinity have redshift profiles similar to those in a vicinity of the axial rays in the axially symmetric case. This indicates that rays generating infinite blueshifts exist also in general QSS spacetimes.
A. Krasinski
Fri, 8 Apr 16
36/54
Comments: 20 pages, 19 figures
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