Huge Filaments as Regions of Space-Time Deformation

Huge Filaments as Regions of Space-Time Deformation Irina Rozgacheva All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences (VINITI RAS), Moscow, Russia E-mail address: rozgacheva@yandex.ru ABSTRACT Huge filaments with scales from several hundred megaparsecs to gigaparsecs are detected in the distribution of galaxies and clusters, quasars, gammabursters. The hypothesis on the nature of the huge filaments as regions of space-time deformation is proposed. An anisotropic deformation of the local region is described by the strain tensor, it depends on the velocities of matter. Galaxies get an extra velocity in the region, which leads to the formation of filamentary structures. The class of exact solution of the GR equations is constructed by introducing the special definition of the Christoffel symbols as function of the velocity of matter. With a definition of these symbols, the motion matter equation turns into identity. For the sake of simplicity, an ideal fluid is considered.


Introduction
It is popularly believed that the dominant structural elements of the large-scale structure are filamentschains consisting of galaxies, groups of galaxies, galaxy clusters, intergalactic gas, and dust. Huge filaments with scales from several hundred megaparsecs to gigaparsecs are detected in the distribution of galaxies and clusters, quasars, gamma-bursters (Great Wall, Great GRB Wall, Hyperion, LQG) [1 -5]. The sizes of these structures are several times greater than the maximum scale length for correlation function of galaxies in standard cosmological CDM model (usually not more than 300 Mpc). The characteristic time of formation of the huge filaments from the initial density contrasts of matter is comparable to or even exceeds the characteristic lifetime of the Universe in the CDM model.
The previous article [6] considered a filament model of primary scalar and vector perturbations of the metric tensor in homogeneous and isotropic cosmology in the framework of the General Theory of Relativity (GR).
This Letter proposes a hypothesis on the relationship of huge filaments with local space-time anisotropy. This anisotropy is described with the strain tensor of space-time. It is assumed that additional velocities of particles of matter correspond to the local anisotropy of space-time, and the strain tensor depends on the velocities of matter. Due to additional velocities, the convergence of world trajectories of matter particles can occur, i.e. the formation of matter flows occurs. Filaments of various scales may be the result of these flows. To describe this picture, a special definition of the Christoffel symbols of the 1st kind as function of the velocity of matter is 3 introduced. With the chosen definition of these symbols, the motion matter equation turns into identity. The metric tensor is determined from the GR equations. For the sake of simplicity, an ideal fluid is considered. Note, that examples of using the strain tensor for the analysis of cosmological models with rotation are considered in the monograph [7].
The astronomer Eddington wrote that the Christoffel symbols are observable physical characteristics of the gravitational field (gravitational field strength) a hundred years ago [8]. In the physical sense, they are primary with respect to the metric tensor of space-time. Here, this Eddington's idea is implemented in the following logical chain: giant filaments are associated with the velocities of the matter flowsthe matter flows are associated with the deformation of space-time -the Christoffel symbols are determined through the speeds of matter. We note that in the modern theory of gauge fields, the Christoffel symbols are determined from equations of the Yang -Mills type for these fields, and the metric tensor is determined from the GR equations.

The strain tensor of space-time
Consider the perfect fluid with the energy-momentum tensor ik where an energy density of fluid is  , four-dimensional velocity is i u , and , the lateen indices run through the values 0, 1, 2, 3, the metric signature (+ ---).
Here, the physical system of units is maintained. To describe the deformation of space-time, we will use the technique developed in the deformation theory of continuous matter. Suppose, due to deformation in the vicinity of the world point i x a coordinate differential i dx increases by a shift i dy : Here, the strain tensor is introduced: (1) The It can be seen from formula (2) The anisotropic strain tensor is determined by the following formula: The velocity of the relative displacement of the world lines of matter particles is calculated using the formula: In the general case, the direction of velocity k W does not coincide with the direction of velocity k u , therefore, the world lines of particles (geodesic lines of space-time) are curved relative to world lines in space-time without anisotropic deformation. This leads, in particular, to the convergence of the world lines of particles in the direction of speed (6) and the formation of elongated structures.

Determination of the Christoffel symbols
Using direct calculations, we can see that the equation of continuity of and the motion equation  Note, that when we consider the homogeneous and isotropic cosmological models, the form of the metric tensor The equation (9) (10) The The Ricci tensor for the coefficients (8)