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.

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.

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 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.

scholarly journals Generalized transformations and coordinates for static spherically symmetric general relativity

2018 ◽  
Vol 5 (4) ◽  
pp. 171109
Author(s):  
James M. Hill ◽  
Joseph O'Leary
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Weak Field ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Weak Field Limit ◽  
Spherically Symmetric Solution ◽  
Coordinate Singularity ◽  
Orthogonal Line

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington–Finkelstein transformation and the Kruskal–Szekeres coordinates.

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.

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.

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

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.

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