Gamma radiation from areal radius minima in a quasi-spherical Szekeres metric

Abstract

In previous papers it was shown that in a quasi-spherical Szekeres (QSS) metric, impulses of gamma radiation can arise that have several properties in common with the observed gamma-ray bursts. This happens when the bang-time function $t_B(r)$ has a gate-shaped hump around the origin of the QSS region. The gamma rays arise along two preferred directions of the QSS geometry (coincident with dipole extrema when axially symmetric, otherwise unrelated). In these directions, the rays of the relic radiation are blueshifted rather than redshifted. The blueshift is generated in a thin region between the Big Bang (BB) and the extremum-redshift hypersurface (ERH). But the Szekeres models can describe the real Universe only forward in time from the last-scattering hypersurface (LSH) because the matter in them has zero pressure. The ERH is tangent to the BB at the origin, so in a neighbourhood thereof the ERH lies earlier than the LSH and no blueshift is generated in the physical region. The question thus arose whether the BB and ERH can be ``unglued'' if the QSS region has no origin, but the areal radius function $\Phi$ has a local maximum or minimum somewhere. In the present paper it is demonstrated that this is indeed the case. If the hump in $t_B(r)$ is centered around the minimum of $\Phi$, then the BB and ERH in general do not coincide there and a stronger blueshift is generated on rays passing nearby. It follows that a lower and narrower hump on the BB set can generate sufficient blueshift to move the initial frequencies of the relic radiation to the gamma range. These facts are demonstrated by numerical calculations in an explicit example of a QSS region.