On conformally related fields in Rosen's bimetric gravitation theory

It is shown that the gravitational energy generation vector is conformally invariant. The necessary and sufficient condition for the conformai invariance of the gravitational field equations is found. The conformal transformations of two simple nongravitational energy tensors are considered. It is shown that the conformal factor for metrics conformal to the background is the solution of a simple differential equation.     

Plane waves in the bimetric gravitation theory

Field equations for plane waves are set up and some solutions are obtained. Transverse, longitudinal, and mixed waves are possible. In the purely transverse case the energy density is positive definite. In the purely longitudinal case it may be negative. However, in one example investigated it is positive if the Riemannian metric tensor satisfies a condition corresponding to space-time having satisfactory physical properties.     

On the conformal transformations of metrics in Rosen's bimetric gravitation theory

The conformal transformations of the background metric are considered and the transformed expressions of the gravitational energy and of the gravitational field equations are obtained. The conditions of conservation of the nongravitational energy are formulated with respect to the transformed metric. Then the background and the physical metrics are both subjected to transformations and the relationship between the corresponding conformal factors analyzed, particularly in the case of conserved nongravitational energy.     

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.     

Some cosmological models in the bimetric theory of gravitation

It is shown that the field equations of the bimetric theory of gravitation have solutions corresponding to a class of homogeneous isotropic cosmological models with negative spatial curvature (k=–1). Some examples are given.     

Minicompact objects according to the bimetric theory of gravitation

It is shown that, similarly to general relativity, the bimetric theory of gravitation predicts the formation of primordial minicompact objects. Contrary to general relativity, however, it predicts that such objects are stable. Observational consequences are discussed.In partial fulfillment of the requirements for the D.Sc. degree.     

Extremality of mass in the bimetric theory of gravitation

In the bimetric theory of gravitation, the static spherically symmetric case involving matter characterized by density and pressure is considered. It is found that the condition that the mass be stationary under small variations of the field variables (including the density) for a fixed number of baryons leads to the field equations and to the equilibrium condition. If one considers only solutions of the field equations, then the mass for a fixed baryon number is stationary (one can expect it to be extremal in most cases) if the equilibrium condition holds.Dedicated to Achille Papapetrou on the occasion of his retirement.     

Magnetized cosmological models in bimetric theory of gravitation

Bianchi type-III magnetized cosmological model when the field of gravitation is governed by either a perfect fluid or cosmic string is investigated in Rosen’s [1] bimetric theory of gravitation. To complete determinate solution, the condition, viz., A=(BC) ⁿ , where n is a constant, between the metric potentials is used. We have assumed different equations of state for cosmic string [2] for the complete solution of the model. Some physical and geometrical properties of the exhibited model are discussed and studied.     

A charge of finite size in the bimetric gravitation theory

The bimetric gravitational field of a charged finite body is derived using a method of approximation. It is found that, with certain exceptions, every charged body has a minimum size, beyond which the field variables become singular. For elementary particles this minimum radius is negligibly small.     

Equations of motion in Rosen's bimetric theory of gravitation

The paper contains an investigation of Rosen's bimetric theory of gravitation in the case of slow velocities and weak fields. Newtonian and post-Newtonian approximations are obtained. The post-Newtonian equation of motion is integrated for an insular system of spherical bodies that move translationally at large mutual distances. It appears that the post-Newtonian law of motion obtained in this way contains terms that depend on the self-energy of the test body (a self-influence phenomenon). It is proved that also in the Einsteinian gravitation this influence is present, but it can be canceled out from the post-Newtonian law of motion if one takes into account the de Donder conditions. The self-influence discovered here seems to be a general gravitation phenomenon, which usually appears in theories of gravitation in the post-Newtonian approximation.     

A gauge-covariant bimetric tetrad theory of gravitation and electromagnetism

In order to get to a geometrically based theory of gravitation and electromagnetism, a gauge covariant bimetric tetrad space-time is introduced. The Weylian connection vector is derived from the tetrads and it is identified with the electromagnetic potential vector. The formalism is simplified by the use of gauge-invariant quantities. The theory contains a contorsion tensor that is connected with spinning properties of matter. The electromagnetic field may be induced by conventional sources and by spinning matter. In absence of spinning matter, the equations are identical with those of the gauge-covariant bimetric theory.⁽²³⁾     

Nonstatic spherically symmetric space-times in Rosen's bimetric gravitation theory

Time dependent metrics, conformally equivalent to the static spherically symmetric metric, are considered. The one-body problem is investigated and some general conditions for accelerated and geometrically modified orbiting are obtained. The radial and nonradial null geodesics are investigated and it is shown that their differential equations are not modified by the conformal factor.     

Inertial and gravitational masses in the bimetric theory of gravitation

The inertial mass of a static spherically symmetric body is evaluated in the framework of Rosen's bimetric theory of gravitation. It is shown that the inertial mass equals the gravitational mass independently of the specific equation of state chosen, and hence that the theory satisfies the equivalence principle.     

The field of a charge in the bimetric gravitation theory

The field equations of the bimetric theory of gravitation are solved for the static, spherically symmetric electric and gravitational fields due to a point charge, subject to certain restrictions.     

The two-body problem in Rosen's bimetric theory of gravitation

This is a continuation of a previous paper, in which the field equations in successive approximations and the post-Newtonian equations of motion in Rosen's theory of gravitation were derived. In this paper the energy integral and the center of mass for an insular system with an arbitrary structure are obtained in the post-Newtonian approximation. A many-body system is considered, and in the extreme case of point bodies (particles) the center-of-mass coordinates are found to be identical with the Einsteinian ones. The two-body problem is considered. For a system of two identical neutron stars of mass 1.3M (a possible model of the Hulse-Taylor binary pulsar system) the trajectory and the perihelion precession are calculated. It is found that the expressions obtained depend on the gravitational self-energy of the stars. The relations deduced from Rosen's bimetric gravitation in the case of small velocities and weak fields are compared with those of general relativity.In partial fulfillment of the requirements for Dr.Sc. degree at the Technion-Israel Institute of Technology.     

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.     

Strong-field effects and time asymmetry in general relativity and in bimetric gravitation theory

The concepts underlying our present theoretical understanding of the radiative two-condensed-body problem in general relativity and in bimetric gravitation theory are critically reviewed. The relevance of the 1935 Einstein-Rosen bridge article is emphasized. The possibility (first suggested by N. Rosen, for the linearized approximation) of extending to gravity the Wheeler-Feynman time-symmetric approach is questioned.     

On the Goldstonic gravitation theory

The physical specificity of gravity as a Goldstone-type field responsible for spontaneous breaking of space-time symmetries is investigated and extended up to supergravity. Problems of the Higgs gravitation vacuum and its matter sources are discussed. A particular “dislocation” structure of a space-time due to Poincaré translation gauge fields and the corresponding modification of Newton’s gravitational potential are predicted.     

On Sakharov's theory of gravitation

The Sakharov theory of gravitation is examined from the viewpoint of the analogy between gravitation and elasticity. It is found that, by using the Cattaneo-Zel'manov projection technique, the deformation tensor connected with the gravitational field can be considered the deformation tensor of a suitable elastic medium. By supposing that transversal waves propagate in this medium with velocityc, one can find an explicit expression for the time dependence of the gravitational constant. Some applications of cosmological interest are briefly discussed.