Szekeres Models Research Articles

Volume averaging in the quasispherical Szekeres model

This paper considers volume averaging in the quasispherical Szekeres model. The volume averaging became of considerable interest after it was shown that the volume acceleration calculated within the averaging framework can be positive even when the local expansion rate decelerates. This issue was intensively studied within spherically symmetric models. However, since our Universe is not spherically symmetric similar analysis is needed in non-symmetrical models. This papers presents the averaging analysis within the quasispherical Szekeres model which is a non-symmetrical generalisation of the spherically symmetric Lemaître–Tolman family of models. In the quasispherical Szekeres model the distribution of mass over a surface of constant t and r has the form of a mass-dipole superposed on a monopole. This paper shows that when calculating the volume acceleration, ä, within the Szekeres model, the dipole does not contribute to the final result, hence ä only depends on a monopole configuration. Thus, the volume averaging within the Szekeres model leads to literally the same solutions as those obtained within the Lemaître–Tolman model.

Geometry and topology of the quasiplane Szekeres model

This paper is a revised version of arXiv:0805.0529 and Phys.Rev. D78, 064038 (2008), taking into account the erratum published in Phys.Rev. D85, 069903(E) (2012). Geometrical and topological properties of the quasi-plane Szekeres model and of the plane symmetric dust model are discussed. Some related comments on the quasi-hyperbolical model are made. These properties include: (1) The pattern of expansion in the plane symmetric case, and the Newtonian model that imitates it; (2) The possibility of toroidal topology of the $t =$ const sections in the plane symmetric model; (3) The absence of apparent horizons in the quasi-plane and quasi-hyperbolic models (they are globally trapped); (4) Description of the toroidal topology in the Szekeres coordinates; (5) Interpretation of the mass function in the quasi-plane model.

Physical and geometrical interpretation of theϵ≤0Szekeres models

We study the properties and behavior of the quasipseudospherical and quasiplanar Szekeres models, obtain the regularity conditions, and analyze their consequences. The quantities associated with radius and mass in the quasispherical case must be understood in a different way for these cases. The models with pseudospherical foliation can have spatial maxima and minima, but no origins. The mass and radius functions may be one increasing and one decreasing without causing shell crossings. This case most naturally describes a snakelike, variable density void in a more gently varying inhomogeneous background, although regions that develop an overdensity are also possible. The Szekeres models with plane foliation can have neither spatial extrema nor origins, cannot be spatially flat, and they cannot have more inhomogeneity than the corresponding Ellis model, but a planar surface can be the boundary between regions of spherical and pseudospherical foliation.

Light propagation through large-scale inhomogeneities in the Universe and its impact on cosmological observations

This paper analyses cosmological observations within inhomogeneous and exact solutions of the Einstein equations. In some way the analyses presented here can be freed from assumptions such as small amplitude of the density contrast. The supernova observations are analysed using the Lemaitre–Tolman model and the CMB observations are analysed using the quasispherical Szekeres model. The results show that it is possible to fit the supernova data without the cosmological constant. However if inhomogeneities of sizes and amplitudes as observed in the local Universe are considered, their impact on cosmological observations is small.

Gravitational collapse in higher dimensional Husain space–time

We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure p and density ρ are related by the following relations (i) p = kρ, (ii) \(p = k\rho - \frac{B(v)}{\rho^{\alpha}}\) (variable modified Chaplygin) and (iii) p = kρα (polytropic). We have studied the nature of singularity in gravitational collapse for the above equations of state and also for different choices of the of the parameters k and B namely, (i) k = 0, B = constant (generalized Chaplygin), (ii) B = constant (modified Chaplygin). It is found that the nature of singularity is independent of these choices of different equation of state except for variable Chaplygin model. Choices of various parameters are shown in tabular form. Finally, matching of Szekeres model with exterior Husain space–time is done.

Evolution of cosmic structures in different environments in the quasispherical Szekeres model

This paper investigates evolution of cosmic structures in different environments. For this purpose the quasispherical Szekeres model is employed. The Szekeres model is an exact solution of the Einstein field equations within which it is possible to describe more than one structure. In this way investigations of the evolution of the cosmic structures presented here can be freed from such assumptions as a small value of the density contrast. Also, studying the evolution of two or three structures within one framework enables us to follow the interaction between these structures and their impact on the evolution. Main findings include a conclusion that small voids surrounded by large overdensities evolve slower than large, isolated voids do. On the other hand, large voids enhance the evolution of adjacent galaxy superclusters which evolve much faster than isolated superclusters.

Structure formation in the quasispherical Szekeres model

Structure formation in the Szekeres model is investigated. Since the Szekeres model is an inhomogeneous model with no symmetries, it is possible to examine the interaction of neighboring structures and its impact on the growth of a density contrast. It has been found that the mass flow from voids to clusters enhances the growth of the density contrast. In the model presented here, the growth of the density contrast is almost 8 times faster than in the linear approach.

Gravitational Entropy in Cosmological Models

We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VIh models that admit an isotropic singularity. We also briefly discuss other possible gravitational entropy functions, including an appropriate measure of the velocity dependent Bel-Robinson tensor.

You cannot get through Szekeres wormholes: Regularity, topology, and causality in quasispherical Szekeres models

The spherically symmetric dust model of Lema\^{\i}tre and Tolman can describe wormholes, but the causal communication between the two asymptotic regions through the neck is even less than in the vacuum (Schwarzschild-Kruskal-Szekeres) case. We investigate the anisotropic generalization of the wormhole topology in the Szekeres model. The function $E(r,p,q)$ describes the deviation from spherical symmetry if ${\ensuremath{\partial}}_{r}E\ensuremath{\ne}0,$ but this requires the mass to be increasing with radius, ${\ensuremath{\partial}}_{r}M>0,$ i.e. nonzero density. We investigate the geometrical relations between the mass dipole and the loci of the apparent horizon and shell crossings. We present the various conditions that ensure physically reasonable quasispherical models, including a regular origin, regular maxima and minima in the spatial sections, and the absence of shell crossings. We show that physically reasonable values of ${\ensuremath{\partial}}_{r}E\ensuremath{\ne}0$ cannot compensate for the effects of ${\ensuremath{\partial}}_{r}M>0$ in any direction, so that communication through the neck is still worse than in the vacuum. We also show that a handle topology cannot be created by identifying hypersufaces in the two asymptotic regions on either side of a wormhole, unless a surface layer is allowed at the junction. This impossibility includes the Schwarzschild-Kruskal-Szekeres case.

Density contrast indicators in cosmological dust models

We discuss ways of quantifying structuration in relativistic cosmological settings, by employing a family of covariant density constrast indicators. We study the evolution of these indicators with time in the context of inhomogeneous Szekeres models. We find that different observers (having either different spatial locations or different indicators) see different evolutions for the density contrast, which may or may not be monotonically increasing with time. We also find that monotonicity seems to be related to the initial conditions of the model, which may be of potential interest in connection with debates regarding gravitational entropy and the arrow of time.

Nature of the central singularity in Szekeres models

The occurrence and nature of the central naked singularity in aspherical Szekeres models is investigated here, and the strength of the singularity is discussed. The implications for the cosmic censorship hypothesis are considered.

The null and KS limits of the Szekeres model

We take the null limit of the Szekeres metric, and obtain a generalization of the Kinnersley rocket metric. It may be viewed as being an inhomogeneous assembly of 2-surfaces that have intrisic spherical, planar or pseudo-spherical symmetry. This new metric inherits many properties of the Szekeres metric, so it has no Killing vectors, no quadrupole moment, and emits no gravitational radiation. We also show that the Kantowski - Sachs-type Szekeres metric is a regular limit of the Lemaître - Tolman type, thus unifying the two Szekeres types.

The gravitational arrow of time and the Szekeres cosmological models

The arrow of time in the Szekeres cosmological models is studied by the use of an invariant depending on the Weyl and Ricci tensors. A vector representing gravitational entropy flux is also introduced. These concepts can be applied satisfactorily to the quasi-spherical models, but their application to the second class of the Szekeres models is somewhat less convincing.

A new approach to inhomogeneous cosmologies: Intrinsic symmetries. III. Conformally flat slices and their analysis

We have already obtained an invariant characterization and classification of the Szekeres inhomogeneous cosmological models. In the present paper, we present a detailed study of the hierarchy of solutions. The approach adopted suggests simple generalizations of the Szekeres models, and we present a number of results and ideas for further study.