Rosen's Bimetric Theory Research Articles

Spherically Symmetric Static Charged Anisotropic Fluid in Rosen's Bimetric Theory of Gravitation

ABSTRACTIn this paper we have obtained an exact solution for the static spherically symmetric space-time with charged anisotropic fluid distribution in context of Rosen's Bimetric General Relativity (BGR).

Spacetime symmetries and topology in bimetric relativity

We explore spacetime symmetries and topologies of the two metric sectors in Hassan--Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress--energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan--Rosen bimetric theory. We emphasize the possibility of imposing ansatzes and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.

CYLINDRICALLY SYMMETRIC COSMIC STRINGS COUPLED WITH MAXWELL FIELDS IN BIMETRIC RELATIVITY

Cylindrically symmetric cosmological models are obtained in Rosen's (1973) bimetric theory, when the source of gravitation is electromagnetic field coupled with one dimensional cosmic string. Some physical and kinematical properties of the model are discussed.

Inhomogeneous Cosmological Models in Bimetric Theory of Gravitation

Plane symmetric inhomogeneous cosmological models for perfect fluid distribution are investigated in the frame work of Rosen's bimetric theory of gravitation. A negative pressure corresponding to false vacuum state is considered. Some of the physical and kinematical properties of the models are discussed.

Bianchi Type-I Massive String Magnetized Barotropic Perfect Fluid Cosmological Model in the Bimetric Theory of Gravitation

We investigate the Bianchi type-I massive string magnetized barotropic perfect fluid cosmological model in Rosen's bimetric theory of gravitation with and without a magnetic field by applying the techniques used by Latelier (1979, 1980) and Stachel (1983). To obtain a deterministic model of the universe, it is assumed that the universe is filled with barotropic perfect fluid distribution. The physical and geometrical significance of the model are discussed. By comparing our model with the model of Bali et al. (2007), it is realized that there are no big-bang and big-crunch singularities in our model and T = 0 is not the time of the big bang, whereas the model of Bali et al. starts with a big bang at T = 0. Further, our model is in agreement with Bali et al. (2007) as time increases in the presence, as well as in the absence, of a magnetic field.

On Kantowski–Sachs Cosmological Models in Bimetric Theory of Gravity

It is shown that Kantowski–Sachs cosmological models do not exist in Rosen's (1973) bimetric theory of gravitation when the source of gravitation is either perfect fluid or cosmic string. Hence, the vacuum model is constructed.

On Plane Symmetric Domain Walls and Cosmic Strings in Bimetric Theory

Plane symmetric thick domain walls and cosmic strings are considered in Rosen's (General Relativity and Gravitation 4, 435, 1973) bimetric theory of gravitation. It is shown that, in this theory, thick domain walls and cosmic strings do not exist. Hence, the vacuum solutions in both the cases are presented.

Inhomogeneous plane symmetric models in bimetric theory

Field equations of Rosen's bimetric theory are obtained with the aid of aninhomogeneous plane symmetric metric in the presence of a perfect fluiddistribution. Models corresponding to vacuum, stiff fluid and disorderedradiation are constructed and discussed.

NON-EXISTENCE OF HIGHER DIMENSIONAL ANISOTROPIC COSMOLOGICAL MODEL IN BIMETRIC THEORY OF GRAVITATION

A Five dimensional spherically symmetric space-time model in Rosen's (1973) bimetric theory of gravitation is considered. It is shown that, in this theory, the geometry of the five dimensional space-time does not admit perfect fluid source. Hence a vacuum model is presented and studied. It is observed that in the case of stiff fluid we again get the vacuum model.

On Some Bianchi Type Cosmological Models in a Bimetric Theory of Gravitation

Spatially-homogeneous and anisotropic Bianchi type-III, V, VI0 cosmological models in Rosen's (1973) bimetric theory of gravitation are considered. It is shown that, in each case, when the soure of the gravitation field is a perfect fluid distribution Bianchi type cosmological models do not exist. Hence vacuum models are presented and studied.

Global parameters of rotating relativistic polytropes in bimetric gravitation theory

We have previously [1] solved the field equations on the basis of bimetric gravitation theory in the first approximation with respect to the angular velocity of rotation in the case of an axisymmetric mass distribution for configurations in which the state of matter is described by a polytropic equation. The present article is a continuation of that work. Here we solve the problem in the second angular velocity approximation, which enables us to determine the corrections to the global characteristics of the rotating configurations, along with the quadrupole moment of a star. Rosen's bimetric gravitation theory (BGT) [2] satisfies the principles of general covariance, local equivalence, and correspondence. The spacet ime manifold is defined by two metrics in BGT:

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.

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.

Non-existence of Biachi type-1 perfect fluid cosmological models in a bi-metric theory of gravitation

It is shown that there do not exist spatially-homogeneous and anisotropic Bianchi type-I cosmological models in Rosen's (1973) bi-metric theory of gravitation when the source of the gravitational field is a perfect fluid distribution. A vacuum cosmological model, in this theory, is presented and studied.

Axially symmetric solution to Rosen's field equations with angular momentum

There has been no Kerr-like solution to Rosen's bimetric theory of gravity, in the sense that there is no stationary, axially symmetric solution with angular momentum term. Here such a solution is derived and investigated.

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.

Some harmonic maps on pseudo-Riemannian manifolds

Rosen's bimetric theory of gravitation, when equipped with a flat background metric, is known to be realized as a harmonic mapping of Minkowski spacetime into a certain homogeneous space. This paper develops and exploits these facts to provide four classes of explicit solutions to Rosen's field equations. These four classes form the elements from which more general solutions may be formed by a type of superposition. It is also shown how spherical gravitational waves may be explicitly built into these solutions.

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.

Stationary axisymmetric gravitational fields in the bimetric theory

Stationary axisymmetric fields are considered in the framework of Rosen's bimetric theory of gravitation. Analytic solutions in the approximation quadratic in the angular velocity are found outside the mass distribution. A method is proposed for finding the metric within the mass distribution and determining the internal structure and the integrated parameters of rotating objects in which the state of the matter is described by a single-parameter equation.

The possible compatibility of Einstein's general theory of relativity, Mach's principle, and Rosen's bimetric theory, in relation to Horák's cosmic potential

Mach's principle is formulated in two different ways, heuristic and mathematical. Known problems of the principle are listed and two of them, the problem of its validity in the case the Universe is open and the boundary condition problem, are analyzed separately. Moreover, the history of the cosmic potential is outlined and a short modification of Horak's deduction of the potential is presented together with a discussion on the conditions of the solution. The conclusions are drawn that the Universe is closed and that Mach's principle is compatible with the general theory of relativity, provided that the Big Bang did not start from a singularity but from finite volume and density. In the last section it is shown that Rosen's bimetric theory is compatible with our picture of the Universe.