Symmetry and Equivalence in Szekeres Models

Abstract

We solve for all Szekeres metrics that have a single Killing vector. For quasi hyperboloidal ($\epsilon =-1$) metrics, we find that translational symmetries are possible, but only in metrics that have shell crossings somewhere, while metrics that can be made free of shell crossings only permit rotations. The quasi planar metrics ($\epsilon =0$) either have no Killing vectors or they admit full planar symmetry. Single symmetries in quasi spherical metrics ($\epsilon =+1$) are all rotations. The rotations correspond to a known family of axially symmetric metrics, which for each $\epsilon$ value, are equivalent to each other. We consider Szekeres metrics in which the line of dipole extrema is required to be geodesic in the 3-space, and show the same set of families emerges. We investigate when two Szekeres metrics are physically equivalent, and complete a previous list of transformations of the arbitrary functions.

16 pages, 3 figures

References in corpus (19)

• Szekeres Swiss-Cheese model and supernova observations
• The Szekeres Swiss Cheese model and the CMB observations
• Structure formation in the quasispherical Szekeres model
• Cosmic spherical void via coarse-graining and averaging non-spherical structures
• Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?
• Redshift propagation equations in the ${\beta }^{\prime }\ne 0$ Szekeres models
• Physical and Geometrical Interpretation of the epsilon <= 0 Szekeres Models
• Exact nonlinear inhomogeneities in $\Lambda$CDM cosmology
• Light propagation in Swiss cheese models of random close-packed Szekeres structures: Effects of anisotropy and comparisons with perturbative results
• Redshift drift in axially symmetric quasi-spherical Szekeres models
• Volume averaging in the quasispherical Szekeres model
• Effect of inhomogeneities on high precision measurements of cosmological distances
• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• Is the shell-focusing singularity of Szekeres space-time visible?
• Modelling Inhomogeneity in Szekeres Spacetime
• Conceptual problems in detecting the evolution of dark energy when using distance measurements
• Thermodynamics in Quasi-Spherical Szekeres Space-Time
• Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models
• Shell Crossing Singularities in Quasi-Spherical Szekeres Models

Cited by in corpus (15)

• Light propagation in Swiss cheese models of random close-packed Szekeres structures: Effects of anisotropy and comparisons with perturbative results
• Intrinsic, deductive, explicit, and algorithmic characterization of the Szekeres-Szafron solutions
• Quantization of inhomogeneous spacetimes with cosmological constant term
• Quantization of the Szekeres System
• Lagrangian theory of structure formation in relativistic cosmology. VI. Comparison with Szekeres exact solutions
• Frame Rotation in the Szekeres Spacetimes
• Thermodynamic class II Szekeres-Szafron solutions. Singular models
• Physical geometry of the quasispherical Szekeres models
• Thermodynamic class II Szekeres-Szafron solutions. Regular models
• A thermodynamic approach to the T-models
• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• Szekeres Universes with GUP corrections
• Rotation, Embedding and Topology for the Szekeres Geometry
• An invariant characterization of the quasi-spherical Szekeres dust models
• Observer-based invariants for cosmological models