# Properties of blueshifted light rays in quasispherical Szekeres metrics

## TL;DR

This paper investigates the properties of blueshifted light rays in axially symmetric quasispherical Szekeres spacetimes, demonstrating how such regions can produce strong blueshifts and affect the apparent size and number of observable sources.

## Contribution

It introduces a model combining Szekeres and Lemaître-Tolman spacetimes to analyze blueshift phenomena, revealing new insights into how inhomogeneities influence light propagation and observations.

## Key findings

- Strong blueshifts occur only along two opposite directions.
- Lowering the Big Bang hump increases the number of observable sources.
- Numerical calculations confirm patterns of redshift and blueshift in the model.

## Abstract

This paper is a follow-up on two previous ones, in which properties of blueshifted rays were investigated in Lema\^{\i}tre - Tolman (L-T) and quasispherical Szekeres (QSS) spacetimes. In the present paper, an axially symmetric QSS deformation is superposed on such an L-T background that was proved, in the first paper, to mimic several properties of gamma-ray bursts. The present model makes $z$ closer to $-1$ than in the background L-T spacetime, and, as implied by the second paper, strong blueshifts exist in it only along two opposite directions. The QSS region is matched into a Friedmann background. The Big Bang (BB) function $t_B(r)$, which is constant in the Friedmann region, has a gate-shaped hump in the QSS region. Since a QSS island generates stronger blueshifts than an L-T island, the BB hump can be made lower - then it is further removed from the observer and implies a smaller observed angular radius of the source. Consequently, more sources can be fitted into the sky - all these facts are confirmed by numerical computations. Null geodesics reaching present observers from different directions relative to the BB hump are numerically calculated. Patterns of redshift across the image of the source and along the rays are displayed.