Szekeres models: a covariant approach

Abstract

We exploit the 1+1+2 formalism to covariantly describe the inhomogeneous and anisotropic Szekeres models. It is shown that an \emph{average scale length} can be defined \emph{covariantly} which satisfies a 2d equation of motion driven from the \emph{effective gravitational mass} (EGM) contained in the dust cloud. The contributions to the EGM are encoded to the energy density of the dust fluid and the free gravitational field $E_{ab}$. We show that the quasi-symmetric property of the Szekeres models is justified through the existence of 3 independent \emph{Intrinsic Killing Vector Fields (IKVFs)}. In addition the notions of the Apparent and Absolute Apparent Horizons are briefly discussed and we give an alternative gauge-invariant form to define them in terms of the kinematical variables of the spacelike congruences. We argue that the proposed program can be used in order to express Sachs' optical equations in a covariant form and analyze the confrontation of a spatially inhomogeneous irrotational overdense fluid model with the observational data.

16 pages, no figures; (v3) few further amendments and some references added, final version to appear in Class. Quant. Gravity

References in corpus (4)

• Multiple non-spherical structures from the extrema of Szekeres scalars
• Is the shell-focusing singularity of Szekeres space-time visible?
• Conceptual problems in detecting the evolution of dark energy when using distance measurements
• Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models

Cited by in corpus (7)

• Symmetry and Equivalence in Szekeres Models
• Quantization of inhomogeneous spacetimes with cosmological constant term
• Frame Rotation in the Szekeres Spacetimes
• Physical geometry of the quasispherical Szekeres models
• Intrinsic Conformal Symmetries in Szekeres models
• Constraining the swiss-cheese IR-fixed point cosmology with cosmic expansion
• Constructing a family of conformally flat scalar field models