Mark Israelit

Background killing vectors and conservation laws in Rosen's bimetric theories of gravitation

The problem of global energy, linear momentum, and angular momentum in Rosens bimetric theories of gravitation is considered from the point of view of motions of the background space-time. It turns out that by means of background Killing vectors global mechanical integrals for matter and field can be defined in a correct manner. For the flat-background bimetric theory conditions are obtained which have been imposed on the algebraic structure of the matter tensorTvμ in order to get global mechanical conservation laws. For bimetric gravitation theories based on a cosmological (nonflat) background the set of Killing vectors is found. For these theories the obtained restrictions on the algebraic structure ofTvμ lead to global generation laws (instead of conservation laws in the flat-background theory) for mechanical quantities. In particular cases the generation effect vanishes and then conservation laws exist. By means of the method developed in this paper, Rosens homogeneous isotropic universe in the framework of the cosmological-background bimetric theory withk=1 is considered. It turns out that such a universe does not generate globally, but will generate locally. The global energy of this universe is found to be zero.

Wesson's induced matter theory with a Weylian bulk

The foundations of Wessons induced matter theory are analyzed. It is shown that the 5D empty bulk must be regarded rather as a Weylian space than as a Riemannian one.The framework of a Weyl-Dirac version of Wessons theory is elaborated and discussed. The bulk possesses in addition to the metric tensor a Weylian connection vector as well Diracs gauge function; there are no sources (mass, current) in the bulk. On the 4D brane one obtains a geometrically based unified theory of gravitation and electromagnetism with mass, currents and equations induced by the 5D bulk

Spherically symmetric fields in Rosen's bimetric theories of gravitation

By means of bimetric Killing vectors two spherically symmetric fields are investigated: (i) the time-dependent one in Rosens flat-background bimetric theory; and (ii) the energy-preserving in Rosens cosmological-background bimetric theory withk = 1. In the first case a wave behavior of the field is present. In the second case a time evolution is obtained for fields, created by insular systems of constant energy. These phenomena are typical for bimetric theories of gravitation.

Weyl-Dirac geometry and dark matter

Weyl proposed a geometry that differed from Riemannian geometry, which underlies general relativity, in that it contained a vector that could be interpreted as describing the electromagnetic field. Dirac modified this geometry to remove certain difficulties and based it on a variational principle which gave satisfactory field equations for gravitation and electromagnetism. However, by changing the value of a parameter appearing in his variational principle one gets, instead of electromagnetism, a field of massive particles of spin 1, which can be assumed to interact with ordinary matter only through gravitation. It is suggested that these bosons, called weylons, provide most of the dark matter in the universe.

A spatially-flat cosmological model

Recently a homogeneous cosmological model free from singularities was proposed, based on the general relativity theory. It described a closed universe (k = +1), initially filled with prematter, characterized by a density ρ equal to the Planck density and a pressureP = −ρ, and undergoing oscillations. In the present work the case of a similar, but spatially flat, universe (k = 0) is investigated. In this case there is an initial geometric singularity (the scale factorR = 0), but not a physical one, since the initial density is finite. This universe begins its existence at a timet = −∞ and, after going through the prematter and radiation-dominated eras, reaches the matter-dominated state and continues to expand indefinitely.

Quintessence and Dark Matter Created by Weyl–Dirac Geometry

A spatially closed universe undergoing at present accelerated expansion, having a non-vanishing cosmological constant, and filled with luminous- and dark matter is described in terms of the Integrable Weyl–Dirac theory. It is shown that, during the dust-dominated period, dark matter and the quintessence pressure, the latter giving rise to acceleration: both are created by the Dirac gauge function. The behavior of two models: a nearly flat one and a well closed are considered in appropriate gauges, and plausible scenarios are obtained. The outcome of the present paper, together with results of a previous work,(31) provide a geometrically based, classical, singularity-free model of the universe, that has originated from a pure geometric Weyl–Dirac entity, passed a prematter period, the radiation-dominated era, and continues its development in the present dust period.

Cosmic dark matter and Dirac gauge function

It is suggested that the dark matter of the universe is due to the presence of a scalar field described by the gauge function introduced by Dirac in his modification of the Weyl geometry. The behavior of such dark matter is investigated.

Perturbations in a singularity-free cosmological model

The work is based on a singularity-free model of the universe previously proposed by the authors. According to this model, at the beginning of the present expansion phase the universe was filled with prematter for which P = -rho, and rho is about rho(p), the Planck density, and the prematter went over to ordinary matter in the course of time. Two approaches are considered. In the first it is assumed that there are initial perturbations in the prematter. These grow tremendously in the course of time. In the second it is assumed that the prematter has no perturbations, but that perturbations develop as the prematter is converted to ordinary matter. 12 refs.

Bimetric killing vectors and generation laws in bimetric theories of gravitation

The concept of bimetric Killing vectors is introduced. The set of these vectors allows one to define global mechanical integrals for matter and field separately, and to get conservation laws for the matter quantities and generation laws for the field quantities. It is possible to predict what physical spaces of high mobility are contained in a certain variant of a bimetric theory. The procedure is developed in the framework of Rosens bimetric theories of gravitation, but it may be applied to a wide class of bimetric theories.

Newton's laws in a cosmological model

A solution of the Einstein field equations is found for the case of a massive particle at rest in a universe which without the particle would be homogeneous, isotropic, and spatially flat. The presence of the particle does not affect the mass density but does change the pressure of the cosmic matter. The metric is expanded in terms of a small parameter. The motion of a test particle, described by the geodesic equations, is compared with that given by Newtons equations if the particle speed is very small compared to that of light. The comparison is made using two different sets of coordinates