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

The problem of global energy, linear momentum, and angular momentum in Rosen's 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 tensorT _v 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 ofT _v 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, Rosen's 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.     

A bimetric machian approach to gravitation

We propose a bimetric machian approach to gravitation with a mathematical structure much simpler than the one of Rosen's bimetric theories. We obtain two cosmological models based on the simplest assumption that the Universe be filled of pure dust matter. One of the two cosmological models is compatible with the currently observed value of the density of dust matter, and provides an age of the Universe which is of the order of the inverse of the present Hubble parameter. One also obtains the Schwarzschild-like solution and its Newtonian limit together with the modified three Kepler laws which allow us to find that presently 0.5×10^?10 (yr)^?1 δ(A/A)δ 0.625×10^?10 (yr)^?1, a denoting the semimajor axis of the orbit of the test particle. Lastly we obtain the Newtonian limit of the theory.     

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 Rosen's bimetric theories of gravitation, but it may be applied to a wide class of bimetric theories.     

Non-existence of higher dimensional axially symmetric field in Rosen's theory of gravitation

In Rosen's bimetric theory of gravitation the non-existence of higher dimensional axially symmetric massive scalar field and massive complex scalar field coupled with electromagnetic field is established.The authors are thankful to the referee for helpful suggestions.     

On Kantowski-Sachs Cosmic Strings Coupled with Maxwell Fields in Bimetric Relativity

Kantowski-Sachs model is studied with source cosmic cloud strings coupled with electromagnetic field in Rosen’s (Gen. Relativ. Gravit. 4:435, 1973) bimetric theory of relativity. It is shown that there is no contribution from Maxwell fields in this theory. Hence geometric string and vacuum cosmological models are established.     

SU(2) × SU(2) Electroweak Theory II: Chiral and Vector Fields on the Physical Vacuum

In this letter a discussion is offered on how symmetry breaking of a theory with twisted bundle of two chiral SU(2) bundles leads to a set of gauge potentials from each group on the physical vacuum that are vector and chiral. The result is that symmetry breaking of this theory leads to massive A ³ transverse modes of the 3-photon along with electromagnetic photons plus the massive neutral and charged weakly interacting bosons. The electromagnetic sector is demonstrated to be a massless vector field and the remainder is a broken chiral field theory.     

Bianchi Types V and VI<Subscript>0</Subscript> Cosmic Strings Coupled with Maxwell Fields in Bimetric Theory

Spatially homogeneous Bianchi types V and VI₀ cosmological models are studied with source cosmic cloud strings coupled with electromagnetic field in Rosen’s (Gen. Relativ. Gravit. 4:435, 1973) bimetric theory of relativity. It is observed that Bianchi type V space time is feasible whereas Bianchi type VI₀ is not feasible. In the feasible case different equations of state for cosmic strings with Maxwell fields do not survive in this theory and the space-time turns out to be flat.     

On Bianchi-I cosmic strings coupled with Maxwell fields in bimetric relativity

Axially symmetric Bianchi-I model is studied with source cosmic cloud strings coupled with electromagnetic field in Rosen’s bimetric theory of relativity and observed that there is no contribution from cosmic strings and Maxwell fields in this theory.     

Does gravitational radiation exist?

An attempt is made to extend the Wheeler and Feynman absorber theory of electromagnetic radiation to the case of the gravitational field (described by the Einstein linear weak-field equations) on the assumption that the source is at the center of a sphere of matter having a density equal to the average density in the universe and a radius equal to the reciprocal of the Hubble constant. It is found that near the source the field of the matter is negligible compared to that of the source, so that one can conclude that the gravitational field generated by the source is time-symmetric (one-half advanced plus one-half retarded). One can conclude that a physical system does not lose energy as gravitational radiation, although a gravitational wave detector may record signals. It appears that there are no periodic running waves in nature, and hence no gravitons. These considerations hold also in the bimetric gravitation theory.     

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 Rosen's flat-background bimetric theory; and (ii) the energy-preserving in Rosen's 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.     

Slow rotation in the bimetric theory of gravitation

The equations describing the moment of inertia and the dragging of inertial frames of slowly rotating neutron stars are derived according to Rosen's bimetric theory of gravitation. Numerical calculations of the properties of neutron stars according to the bimetric theory and general relativity were made using several equations of state. The general trend found is that in the bimetric theory neutron stars with a given mass induce a smaller dragging of inertial frames than in general relativity. The moment of inertia of low-mass stars also is smaller in the bimetric theory. For high-mass stars, however, the moment of inertia is found to be larger in the bimetric theory.In partial fulfillment of the requirements for the D.Sc. degree.     

A note on the strengths of singularities in the Einstein-Cartan theory

In general relativity bounds were given on the possible divergency rates of the elements and of the trace of the tidal-force tensorR _abcdu^bu^d along incomplete maximal causal geodesics. These results are transformed into the Einstein-Cartan theory and are illustrated with two simple examples of spacetimes filled with charged spinless and spinning perfect fluids interacting with electromagnetic field.     

Matter induced bimetric actions for gravity

The gravitational effective average action is studied in a bimetric truncation with a nontrivial background field dependence, and its renormalization group flow due to a scalar multiplet coupled to gravity is derived. Neglecting the metric contributions to the corresponding beta functions, the analysis of its fixed points reveals that, even on the new enlarged theory space which includes bimetric action functionals, the theory is asymptotically safe in the large N expansion.     

A charged particle in bimetric general relativity

The gravitational field of a charged particle is investigated on the basis of the bimetric general relativity theory. It is found that the field differs from the Reissner-Nordström field only very close to the sphereR=m+(m ² –Q ²)^1/2. This sphere is impenetrable, and its interior is unphysical.     

Doubly coupled matter fields in massive bigravity

In the context of massive(bi-)gravity,non-minimal matter couplings have been proposed.These couplings are special in the sense that they are free of the Boulware-Deser ghost below the strong coupling scale and can be used consistently as an effective field theory.Furthermore,they enrich the phenomenology of massive gravity.We consider these couplings in the framework of bimetric gravity and study the cosmological implications for background and linear tensor,vector,and scalar Previous works have investigated special branches of solutions.Here we perform a complete perturbation analysis for the general background equations of motion,completing previous analyses.     

The scale-transformation of electromagnetic theory and its applications

The scale-transformation of electromagnetic theory is investigated in detail based on the form of Maxwell equations in scale-transformation being unchanged in different coordinate systems. The relations of electromagnetic parameters in a rectangular coordinate system and in a spherical coordinate system are presented respectively. The scale-transformation invariants for electromagnetic field are derived and their physical meaning is also presented. It is indicated by simulation that the electromagnetic waves located in medium can be considered to be isotropic due to the fact that the size of propagating vector affected by the scale factors and observing azimuth is on a size of 10^-9, which provides a new approach for investigating the electromagnetic characteristics of ellipsoidal targets.     

Conservation laws in Bimetric gravitation theories

In the bimetric theory of gravitation with a flat-space background metric conservation laws for energy and momentum are considered in several different forms. In the bimetric theory with a constant-curvature background metric a previous error in the energy-momentum relation is corrected.     

Axially Symmetric Cosmological Model with Wet Dark Fluid in Bimetric Theory of Gravitation

The purpose of this paper is to investigate the role of wet dark fluid in axially symmetric cosmological model within the frame work of bimetric theory of gravitation proposed by Rosen (Gen. Relativ. Gravit. 4:435, 1973). In this theory, it is observed that there is no contribution from wet dark fluid.     

Strings in a conformally invariant theory of gravitation and electromagnetism

A recently proposed unified theory of gravitation and electromagnetism is studied in the weak field approximation and conformally flat gauge. It requires the photon to have a mass real or imaginary (Meissner effect) depending on the sign of the cosmological constant λ, and proportional to λ^{$\text{1}\text{2}$}. Thus the range of the electromagnetic interaction must be greater than ～2 × 10²⁷ cm. The electromagnetic field is entirely of topological origin, strings are present in the theory and the flux of the electromagnetic field is quantized. A classical normalization condition for the potential makes the flux quantum equal to ± e, while the fine structure constant provides a scale for the rate of change in the length of a vector displaced around a closed path linking the flux.