Relativistic Theory Of Gravitation Research Articles

Relativistic theory of gravity and a Brans-Dicke scalar field

The natural generalization of the relativistic theory of gravity (RTG) by incorporating a Brans-Dicke scalar field is discussed. The equation for a scalar-tensor gravitational field in Minkowski space and the expression for the total energy-momentum metric tensor of a gravitational field and nongravitational matter is derived from the variational principle with a gravitational Lagrangian quadratic in the first derivatives of the scalar and tensor gravitational potentials. The two-parameter spherically symmetrical static solution for vacuum equations with a zero mass tensor graviton was obtained. This solution has a true singular Schwarzschild surface. In the case of a nonzero mass graviton, an approximate nonsingular solution for the beginning of the universe was obtained. It is noted that in the frame of the scalar-tensor generalization of RTG, a nonsingular homogeneous isotropic cosmology can be represented, not only by cyclic models, but also by models with an infinitely expanding universe and a simultaneously decreasing gravitational scalar.

On the constraint equation in the relativistic theory of gravitation

Expressions for covariant and contravariant components of the metric tensor for the effective Riemann space-time and for its determinant are constructed on the basis of the relations of tensor algebra.

Post-Newtonian approximation in the relativistic theory of gravity

Based on the RTG equations, a simple derivation of the post-Newtonian approximation is presented. A comparison is made of the calculations of gravitational effects in the solar system based on RTG and on the general theory of relativity.

Expanding ball in the scalar field model and in the relativistic theory of gravity

The first-order approximations for the internal and external fields of an expanding ball are evaluated in the scalar field model and in the relativistic theory of gravity. The similarity of the corresponding solutions is pointed out. It is suggested how the nonstatic properties possessed by solutions in the original inertial coordinates can be observed experimentally.

The symmetric tensor field in the relativistic theory of gravitation

The system of a self-gravitating scalar field is frequently used in inflationary cosmological models. In the present paper we study a more complicated system containing an extra linear tensor field ψik=ψki with minimal coupling. We determine five of the six free parameters that occur in the most general expression for the actionSψ of this field. In doing so we assume that in flat space-time the field ψik must be invariant under gauge transformations. In a special case theSψ found becomes a known expression for the action of a massless tensor field ψik. We compute the metric energy-momentum tensor that determines the contribution of ψik to the Einstein equations. We also exhibit the equations of motion of ψik in curved space-time.

Phenomenological approach to the viable nonmetric relativistic scalar 4-vector theory of gravitation

Contrary to the hypothesis that every viable theory of gravitation must be the metric one, this paper presents the example of nonmetric relativistic gravitational theory on the basis of Minkowski space-time, where the gravitation is described by a mixture of the nonlinear scalar field and the linear 4-vector field, compatible with all the known post-Newtonian gravitational tests, with tests on gravitational radiation from binary pulsar PSR 1913 + 16 and with the ordinary cosmological notions.

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce ψL(S)—the gyroscope's precession rate due to the orbital velocity—and ψS(S)—the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are ψL(S) = (2/3)ψL(G), ψS(S) = (3/2) cos β(1 - sin2δ cos2β)1/2ψS(G), where β and δ are the gyroscope's polar angles, and ψL(G) and ψS(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.

The theory of the classical gravitational field

Equations for the massive gravitational field have been derived in the framework of the special theory of relativity on the basis of the geometrization principle. Graviton mass has been shown to be crucial for the elaboration of the relativistic theory of gravitation. According to this theory, a homogeneous and isotropic universe develops in a series of alternating cycles, from high to low density, and cannot be anything other than flat. The theory predicts the presence of a large amount of latent mass in the universe and prohibits the existence of 'black holes'. Also, the theory explains all observable events so far known to occur in the Solar system.

Lagrangian theory of constrained systems: Cosmological application

Previous work in the literature has studied the Hamiltonian structure of anR 2 model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. Within the framework of Dirac's theory, torsion is found to lead to a second-class primary constraint linear in the momenta and a second-class secondary constraint quadratic in the momenta. This paper studies in detail the same problem at a Lagrangian level,i.e. working on the tangent bundle rather than on phase space. The corresponding analysis is motivated by a more general program, aiming to obtain a manifestly covariant, multisymplectic framework for the analysis of relativistic theories of gravitation regarded as constrained systems. After an application of the Gotay-Nester Lagrangian analysis, the paper deals with the generalized method, which has the advantage of being applicable to any system of differential equations in implicit form. Multiplication of the second-order Lagrange equations by a vector with zero eigenvalue for the Hessian matrix yields the so-called first-generation constraints. Remarkably, in the cosmological model here considered, if Lagrange equations are studied using second-order formalism, a second-generation constraint is found which is absent in first-order formalism. This happens since first- and second-order formalisms are inequivalent. There are, however, noa priori reasons for arguing that one of the two is incorrect. First- and second-generation constraints are used to derive physical predictions for the cosmological model.

Can galactic observations be explained by a relativistic gravity theory?

We consider the possibility of an alternative gravity theory explaining the dynamics of galactic systems without dark matter. From very general assumptions about the structure of a relativistic gravity theory we derive a general expression for the metric to order $(v/c)^2$. This allows us to compare the predictions of the theory with various experimental data: the Newtonian limit, light deflection and retardation, rotation of galaxies and gravitational lensing. Our general conclusion is that the possibility for any gravity theory to explain the behaviour of galaxies without dark matter is rather improbable.

Binary pulsars and relativistic gravitation

Radio pulsars, which are rapidly rotating, highly magnetized neutron stars, are known to be extraordinarily precise `celestial clocks' with a variety of applications in astrophysics and fundamental physics. The pulsars found in close binary systems, especially those with massive () compact companions, have proved to be excellent tools of experimental gravitation. Moving in eccentric orbits at mildly relativistic speeds (), having surface potentials of the order of (compared to for the Sun), the high-mass binary pulsars are, in fact, the best known probes of relativistic gravity. Precise timing measurements of the first relativistic binary pulsar, SCR B1913+16, discovered by Hulse and Taylor in 1974, have led to establishing the most convincing evidence, so far, that the quadrupolar gravitational waves exist. This and several other, later discovered binary pulsars have defined a distinct class of celestial objects characterized by the presence of measurable relativistic effects in their orbital motion. Timing observations of binary pulsars provide a method to detect these effects and to apply them in the tests of general relativity and other gravity theories in strong-field conditions.

Scalar gravitation: A laboratory for numerical relativity. II. Disks.

While not a correct physical theory, relativistic scalar gravitation provides a simple test site for developing many of the tools of numerical relativity. Using this theory, we have built a mean-field particle simulation scheme to study the dynamical behavior of collisionless disks. Disks are one-dimensional matter sources of two-dimensional gravitational fields. One-dimensional disk sources can be evolved without excessive computational resources and yet they are able to generate nonspherical gravitational waves. We find that we are able to calculate smooth and accurate wave forms from time-varying disks, despite the stochastic representation of the matter source terms caused by sampling with a finite number of particles. A similar scheme should provide accurate wave forms in general relativity, provided sufficient computer resources are used.

Scalar gravitation: A laboratory for numerical relativity. III. Axisymmetry.

We construct a two-dimensional axisymmetric mean-field particle simulation scheme that solves the equations of relativistic scalar gravitation coupled to collisionless matter. Although scalar gravitation theory disagrees with experiment, it is useful as a testing ground for numerical methods used to solve the equations of general relativity, particularly in the generation of gravitational waves. We discuss methods for extracting the gravitational wave amplitude from the field variables, as well as methods for imposing an accurate outgoing-wave boundary condition on the scalar field at a finite radius. We find that for continuous matter distributions, our code is able to calculate smooth and accurate gravitational wave forms, despite the stochastic representation of the matter source terms caused by sampling with a finite number of particles. A similar scheme should provide accurate wave forms in general relativity, provided sufficient computer resources are used.

On the origin of inertial accelerations

Are inertial forces of gravitational origin? The standard geometric interpretation of the general theory of relativity may be employed to show that inertial effects cannot be caused by the gravitational influence of distant masses. The same would hold in any metric theory of gravity that combines local Lorentz invariance with Newtonian gravitation as in general relativity. In fact, the status of the origin of translational inertial accelerations in the relativistic theory of gravitation is similar to that in Newtonian mechanics.

A Viable Model of Locally Anisotropic Space-Time and the Finslerian Generalization of the Relativity Theory

The work is devoted to the construction of a viable model of locally anisotropic, i.e. Finslerian, space-time and to the generalization, on this basis, of the relativistic theory of gravitation. Arguments in favour of this model are considered. From physical considerations the concrete form of the Finslerian metric has been reconstructed and within the framework of the correspondence principle a formalism of the theory has been developed. The approach suggested is aimed at developing unified gauge theories of all fundamental interactions. Much attention is given to the nontrivial physical manifestations of local space anisotropy and to the possibility of its experimental detection.

Evolution of Friedmann universe in the relativistic theory of gravitation based on spaces of constant curvature

A study is made of the evolution of a homogeneous and isotropic universe (Friedmann universe) in the framework of the relativistic theory of gravitation based on a space of arbitrary constant curvature. Six types of possible background space are considered. For four of them, a detailed investigation of the asymptotic solutions of the evolution equations is made. The cosmological scenarios corresponding to different choices of the background space are described.

First experiment to test whether space-time is flat

From both special and general relativistic gravitational theories, we deduce the predicted value of the precessional angular velocity of a gyroscope caused by the additional gravitational field due to the earth's rotation. The orbiting gyroscope experiment will be the first to test whether space-time is flat.

Scalar gravitation: A laboratory for numerical relativity.

While not a correct physical theory, relativistic scalar gravitation provides a simple test site for developing many of the tools of numerical relativity. In contrast with general relativity, scalar gravitation allows gravitational waves to be generated in spherical symmetry. Hence one needs only one spatial dimension to try out methods of calculating wave emission and propagation. Using this theory, we have built a mean-field particle simulation scheme to study the dynamical behavior of collisionless matter in spherical symmetry. We find that we are able to calculate smooth and accurate wave forms, despite the stochastic representation of the matter source terms caused by sampling with a finite number of particles. A similar scheme should provide accurate wave forms in general relativity, provided sufficient computer resources are used.

The poloidal field of a slowly rotating axisymmetric rotator (An axisymmetric rotator magnetosphere)

Abstract The equation governing the poloidal field of an axisymmetric rotator is derived. The equation is obtained in the MHD approximation with allowance for relativistic effects, plasma pressure and gravitation of the central object. The problem of cold plasma ejection from the magnetosphere of an axisymmetric rotator at small angular velocities is solved with the help of this equation. Rotation is considered as a small perturbation of a magnetosphere. An analytical expression for the corrections to the poloidal magnetic field is obtained. The solution shows a poleward deflection of the flow due to the magnetic force of spiraling field lines.

Resource Letter RP-1: Radio pulsars

This Resource Letter provides a guide to the literature on radio pulsars. Papers at elementary (E), intermediate (I), and advanced (A) levels are cited. Historically important papers, including relevant articles published before the discovery of pulsars in 1967, are listed, as are current areas of pulsar research. This guide also includes a discussion of pulsars’ use in studying a variety of other phenomena ranging from the interstellar medium to relativistic theories of gravitation.