On a conformal theory of gravitation

1967 ◽  
Vol 63 (3) ◽  
pp. 809-817 ◽  
Author(s):  
Jamal N. Islam
Keyword(s):  
Explicit Solution ◽  
Special Form ◽  
Gravitational Constant ◽  
Special Solution ◽  
Field Equations ◽  
Conformal Theory ◽  
Theory Of Gravitation

AbstractRecently Hoyle and Narlikar(2) have put forward a conformal theory of gravitation in which they obtain an explicit solution of the field equations using certain approximations and assumptions of symmetry. To obtain the solution, the metric is assumed to have a special form. In the present paper a more general form of the metric is considered, and it is shown that many of the features of the special solution are shared by the solution in the more general case. In particular, the implications of the special solution as concerns the sign of the gravitational constant remain valid in the more general case under certain assumptions.

Field equations in the neighbourhood of a particle in a conformal theory of gravitation

1968 ◽  
Vol 306 (1487) ◽  
pp. 487-501 ◽  
Keyword(s):  
Boundary Conditions ◽  
Special Solution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Conformal Theory ◽  
Usual Form ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined in detail. This metric is assumed to be of the usual form d s 2 = e v d t 2 —e λ d r 2 — r 2 (d θ 2 + sin 2 θ d ψ 2 ) where λ and v are functions of r only. Hoyle & Narlikar obtained a solution of the field equations under the assumption λ + v = 0. In this paper the case λ + v ǂ 0 is investigated, and it is shown that the only solution that satisfies all the boundary conditions is the special solution obtained by setting λ + v = 0. The significance of this result is discussed.

Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

1969 ◽  
Vol 313 (1512) ◽  
pp. 71-82 ◽  
Keyword(s):  
Local Geometry ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Coordinate Singularity ◽  
Previous Solution ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric ◽  
Radial Variable

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

scholarly journals Dark Energy as a Cosmological Consequence of Existence of the Dirac Scalar Field in Nature

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
O. V. Babourova ◽  
B. N. Frolov
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Early Universe ◽  
Large Time ◽  
Field Equations ◽  
Conformal Theory ◽  
Effective Cosmological Constant ◽  
Theory Of Gravitation ◽  
Cosmological Consequence

The solution of the field equations of the conformal theory of gravitation with Dirac scalar field in Cartan-Weyl spacetime at the very early Universe is obtained. In this theory dark energy (described by an effective cosmological constant) is a function of the Dirac scalar field β. This solution describes the exponential decreasing of β at the inflation stage and has a limit to a constant value of the dark energy at large time. This can give a way to solving the fundamental cosmological constant problem as a consequence of the fields dynamics in the early Universe.

A conformal theory of gravitation

1966 ◽  
Vol 294 (1437) ◽  
pp. 138-148 ◽  
Keyword(s):  
Explicit Solution ◽  
Conformal Transformation ◽  
Einstein Equations ◽  
Fluid Approximation ◽  
Conformal Theory ◽  
Theory Of Gravitation

Certain aspects of the new theory of gravitation proposed in a recent paper are examined in greater detail. It is shown that in the smooth fluid approximation the familiar Einstein equations follow as a result of a specific conformal transformation. The equations of the the theory differ from those of Einstein in the neighbourhood of a particle, however. This is illustrated by means of an explicit solution. Criticisms of the theory by other authors are considered and discussed.

Long range forces and broken symmetries

1973 ◽  
Vol 333 (1595) ◽  
pp. 403-418 ◽  
Keyword(s):  
Gravitational Constant ◽  
Equations Of Motion ◽  
Vacuum Field ◽  
Field Equations ◽  
Field Function ◽  
Closed Loops ◽  
Broken Symmetries ◽  
Action Integral ◽  
Theory Of Gravitation ◽  
Set Up

There are reasons for believing that the gravitational constant varies with time. Such a variation would force one to modify Einstein’s theory of gravitation. It is proposed that the modification should consist in the revival of Weyl’s geometry, in which lengths are non-integrable when carried around closed loops, the lack of integrability being connected with the electromagnetic field. A new action principle is set up, much simpler than Weyl’s, but requiring a scalar field function to describe the gravitational field, in addition to the g μν . The vacuum field equations are worked out and also the equations of motion for a particle. An important feature of Weyl’s geometry is that it leads to a breaking of the C and T symmetries, with no breaking of P or of CT . The breaking does not show itself up with the simpler kinds of charged particles, but requires a more complicated kind of term in the action integral for the particle.

scholarly journals Bianchi Type-VI0 Cosmological Model with Special Form of Scale Factor in Sen-Dunn Theory of Gravitation

2021 ◽  
Vol 13 (1) ◽  
pp. 137-143
Author(s):  
D. Basumatay ◽  
M. Dewri
Keyword(s):  
Cosmological Model ◽  
Special Form ◽  
Bianchi Type ◽  
Scale Factor ◽  
Type I ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Geometrical Properties ◽  
Theory Of Gravitation ◽  
Bianchi Type Vi0

A Bianchi Type-VI0 cosmological model with a special form of scale factor is studied. Einstein field equations in Sen-Dunn theory are obtained and solved for exact solutions. This solution gives a scenario of the dark energy model which tends to a ɅCDM model. The physical and geometrical properties are also obtained and analyzed with the present day observations.

Conformal frames and field equations in a conformal theory of ǵravitation

1970 ◽  
Vol 67 (2) ◽  
pp. 397-414 ◽  
Author(s):  
Jamal N. Islam
Keyword(s):  
Static Solution ◽  
Space Time ◽  
The Other ◽  
Physical Situation ◽  
Field Equations ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Theory Of Gravitation ◽  
Conformal Frames

AbstractSome aspects of the field equations of the conformal theory of gravitation put forward by Hoyle and Narlikar are studied. The field equations are conformally invariant and one can use a particular conformal frame to simplify the equations, since all conformal frames are regarded as physically equivalent. However, some conformal frames may be unsuitable in some regions of space-time, and with the use of such a frame one may get an unphysical solution. The use of conformal frames and the difficulties involved are illustrated by considering a given physical situation in two different conformal frames. The physical situation is that of two isolated particles. A static solution for this situation is obtained in both frames, and it is shown that a property that is quite unphysical in one frame transforms into a physically reasonable property in the other.

scholarly journals Post-Newtonian limit: second-order Jefimenko equations

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
David Pérez Carlos ◽  
Augusto Espinoza ◽  
Andrew Chubykalo
Keyword(s):  
Linear Equations ◽  
Space Time ◽  
Second Order ◽  
Field Equations ◽  
Gravitational Fields ◽  
Mass Distributions ◽  
Minkowski Space Time ◽  
Theory Of Gravitation ◽  
Gravity Probe ◽  
Gravitational Equations

Abstract The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

scholarly journals Quantitative Support for Borowski’s Theory of Gravitation

2013 ◽  
Vol 17 ◽  
pp. 67-71 ◽  
Author(s):  
Michael A. Persinger
Keyword(s):  
Dark Matter ◽  
Gravitational Constant ◽  
Planetary Motion ◽  
Free Oscillations ◽  
Energy Equivalence ◽  
Order Of Magnitude ◽  
Theory Of Gravitation

The Borowski Theory of Gravitation (BTG) indicates that movements of mass such as planets through space are determined by differential pressures from dark matter. One of the consequences of the final epoch is that there would be no matter but only distance. Quantitative solutions indicate that the tensor to set universal average dark matter pressure equal to G, the gravitational constant, would require that the terminal length would be ~2.2∙1069 m or effectively identical to current estimates of energy equivalence of the universal mass. For the earth’s orbit the force from the dark pressure is the same order of magnitude as the force associated with the product of the planet’s mass and background free oscillations whose origins are still ambiguous. The convergences of solutions suggest that the BTG may reveal alternative interpretations and mechanisms for the role of gravitation in planetary motion.

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