Newtonian analogue of force and motion of a free particle in the gravitational field of theC-metric

In the first part of the paper the Newtonian analogue of force for theC-metric has been investigated. To the first-order of approximation in the absence of acceleration of the particle generating theC-metric, one component of the force vector corresponds to the Newtonian analogue of force. In general there are relativistic correction terms due to acceleration term in theC-metric. In the second part of the paper the motion of a freely falling body has been investigated. It is found that plane orbits are not possible. Also the radial fall is not possible and in the equation of the orbit there are terms having no classical analogue. They can be interpreted as the effect of the dragging of the inertial frame produced by the rectilinear acceleration.     

Newtonian analogue of force and motion of a free particle in the gravitational field of Kerr-de Sitter space-time

In the first part of the paper the Newtonian analogue of force for the Kerr-de Sitter metric has been investigated. To the first-order of approximation, a component of the force vector corresponds to the Newtonian gravitational force and a cosmic force arising due to the cosmological constant A. Int the higher order of approximation, the relativistic correction terms due to rotation and the presence of A are obtained. In the second part of the paper the motion of a freely-falling body has been investigated. It is found that plane orbits are not possible. Also a radial fall is not possible and there is a rotational drag on the particle which has no Newtonian analogue.     

A plane symmetric Bianchi type-I inflationary universe in general relativity

A plane symmetric homogeneous space-time in the presence of mass less scalar field with a flat potential is investigated. To get an inflationary universe, we have considered a flat region in which potential V is constant. Some physical and kinematical properties of the model are also discussed.     

Periodic motions in a gravitational central field with a rotating external force

We consider a Kepler problem, with an additional rotating external force, and study the existence of periodic solutions when a small perturbative term is introduced. Surprisingly enough, we always get at least one of such solutions. Moreover, if a nonresonance assumption is added, then the existence of a second solution is also proved.     

Magneto-viscous fluid cosmological model of plane symmetry in general relativity

The object of this paper is to investigate the behaviour of magnetic field in a viscous fluid cosmological model. Various physical and geometrical properties of the model have also been discussed.     

Dynamics of a particle in a gravitational field of a homogeneous annulus disk

We formulate the problem of an infinitesimal particle moving in the space under the influence of the gravitational force induced by a homogeneous annulus disk fixed on a plane. We compute using different coordinates and in terms of an elliptic integral the potential associated to this problem. Also we study the symmetries of the associated potential. After that, we look at the dynamics in some particular cases, namely: in the line perpendicular to the plane that contains the annulus disk and passes through the center of the ring and on the plane that contains the massive annulus.      

Charged particle motion on and off the equatorial plane of a magnetic star in Rosen's bimetric gravity

In this paper we have studied in detail (numerically) the trajectories of charged particles in a magnetic field (dipolar at infinity) associated with a static star in the framework of Rosen's bimetric theory of gravity. It was found that there do exist potential wells that allow possible trapping of particles in stable orbits both on and off the equatorial plane. A particularly interesting feature that has shown up is the fact that the characteristics of the effective potential wellV _eff depend on the ratio of the magnetic field strength parameter λ, and the angular momentumL of the charged particle. For values lower than a critical (λ/L) _c the potential well lies within the regionr≤2m.     

A search and classification of multiple systems in the general field

Summary The general problems are formulated, and the classification of the multiple star and galaxy systems is proposed. The dynamical states of eight nearby triple stars are ascertained. Presented by S. Vereshchagin.     

The problem of motions up to the second post-newtonian approximation in general relativity theory

In this paper we give the Hamiltonian function for aN-body system up to the 2-P.N.A. Then as an example, from the LagrangianL _m of a test particle we derive the equations of its motion up to the 2-P.N.A. in the field of a heavy bodym ₂at rest.     

Elimination of the gravitational singularities within the framework of Einstein's general theory of relativity

In this paper two examples are given, showing that the existence of black holes in the Universe violates, in its consequences, the principle of causality. The solution presented is based on the idea that the primordial black holes have zero-mass-energy and consequently zero-radius of the event horizon. Despite the existence of the surface of last influence, gravitational collapse does not produce black holes during a finite time interval as measured by an external observer. The only singularity, possible to accept (if any), is the initial and final cosmological singularity.     

Why the concepts of a cosmic potential and gravitational force need not be redundant in the general relativity and cosmology

A reply is given to the critique that the introduction of the cosmic potential and gravitational force into the general relativity is, at least, redundant, if not wrong. The introduction is both motivated and necessary, in order to make Mach's principle and the general relativity compatible.     

Product spaceV 2xV 2 and plane fronted waves in general projective relativity

In this paper the field equations of General Projective Relativity have been investigated in the product space ofV ₂xV ₂ space-time (Bertotti, 1959) and plane fronted metric of Peres (1959). It is shown that wave solutions exist in both space-times. In Peres' space we mention two solutions which can be interpreted as plane-monochromatic waves and wave packets, respectively.     

Relation between physical and metric field in general relativity and cosmology

By assuming that the whole matter of the Universe possesses a dilatational degree of freedom, we attempted to show the equivalence between the curvedmetric of space-time and the flat metric of dilated space-time. In the framework of this procedure we supposed that the metrical field and the physical space and time change their roles. The basic result suggests that gravitation and dilatation are interrelated phenomena. In addition we discuss the possibility of the Universe which is of a hybrid type: it possesses at the same time properties of the evolutionary and stationary Universe. Finally, we discuss the lenghtening of day in time as an example which can support our ideas. There was suggested that this phenomenon appears partly as cosmological manifestation.     

Motion of a satellite in the equatorial plane of a spheroid

An exact, closed-form solution of the problem of the motion of a satellite in the equatorial plane of an oblate body is obtained. It is shown that the classic formula for the motion of the perihelion is a first order approximation to the exact formula.     

Notes on applications of general relativity in free space : implication from the motion of a test particle

The equations of motion of a neutral test particle in the field obtained by Wanas (1990) are completely solved. The solution obtained is compared with corresponding solutions in the cases of the Reissner-Nordstrom field, the Kerr field, and the Kerr-Newman field. The comparison shows that the new constant, appeared in the field considered, is connected to electromagnetism and not to spin phenomena.     

Prediction of satellite motions in the Earth's gravitational field with axial symmetry by the KS regularized theory

In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for the KS regularized theory will be established for any numberN of the zonal harmonic coefficient. A general recursive computational algorithm based on these formulae is also established for the initial value problem of the KS theory for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding toN=2 andN=36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.     

Preliminary limits of a logarithmic correction to the Newtonian gravitational potential in binary pulsars

We obtain preliminary limits on a logarithmic correction to the Newtonian gravitational potential by using five binary pulsars:PSR J0737-3039,PSR B1534+12,PSR J1756-2251,PSR B1913+16 and PSR B2127+11C.This kind of correction may originate from fundamental frameworks,like string theories,effective models of gravity due to quantum effects and the non-local gravity scheme.We estimate the upper limit of the Tohline-Kuhn-Kruglyak parameter λ and the lower limit of the FabrisCampos parameter a,which parameterize the correction and are connected to each other by αλ=—1.By analyzing the advances of periastron of these binary pulsars,we find that the preliminary upper limit of α is 0.19±0.14 kpc~(-1) and the preliminary lower limit of λ is-5.2±3.8 kpc.They are compatible with the bounds based on dynamics of spiral galaxies but quite different from those given by solar system dynamics.These results indicate that this logarithmic correction might be more observable in current timings of binary pulsars than in motions of the solar system.     

Gaseous drag on a gravitational perturber in Modified Newtonian Dynamics and the structure of the wake

We calculate the structure of a wake generated by, and the dynamical friction force on, a gravitational perturber travelling through a gaseous medium of uniform density and constant background acceleration   g _ext  , in the context of Modified Newtonian Dynamics (MOND). The wake is described as a linear superposition of two terms. The dominant part displays the same structure as the wake generated in the Newtonian gravity scaled up by a factor  μ⁻¹( g _ext/ a ₀)  , where a ₀ is the constant MOND acceleration and μ the interpolating function. The structure of the second term depends greatly on the angle between   g _ext  and the velocity of the perturber. We evaluate the dynamical drag force numerically and compare our MOND results with the Newtonian case. We mention the relevance of our calculations to orbit evolution of globular clusters and satellites in a gaseous protogalaxy. Potential differences in the X-ray emission of gravitational galactic wakes in MOND and in Newtonian gravity with a dark halo are highlighted.