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.

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. 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.

The renormalisable theory of gravitation and the einstein equations

1976 ◽  
Vol 58 (1) ◽  
pp. 7-8 ◽  
Author(s):  
A.A. Belavin ◽  
D.E. Burlankov
Keyword(s):  
Einstein Equations ◽  
Theory Of Gravitation

scholarly journals Inflation without a trace of lambda

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
John D. Barrow ◽  
Spiros Cotsakis
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Conformal Transformation ◽  
Vacuum Energy ◽  
Einstein Equations ◽  
Scale Invariant ◽  
Field Source ◽  
Scale Theory ◽  
Wide Range

AbstractWe generalise Einstein’s formulation of the traceless Einstein equations to f(R) gravity theories. In the case of the vacuum traceless Einstein equations, we show that a non-constant Weyl tensor leads via a conformal transformation to a dimensionally homogeneous (‘no-scale’) theory in the conformal frame with a scalar field source that has an exponential potential. We then formulate the traceless version of f(R) gravity, and we find that a conformal transformation leads to a no-scale theory conformally equivalent to general relativity and a scalar field $$\phi $$ ϕ with a potential given by the scale-invariant form: $$V(\phi )=\frac{D-2}{4D}Re^{-\phi }$$ V ( ϕ ) = D - 2 4 D R e - ϕ , where $$\phi =[2/(D-2)]\ln f^{\prime }(R)$$ ϕ = [ 2 / ( D - 2 ) ] ln f ′ ( R ) . In this theory, the cosmological constant is a mere integration constant, statistically distributed in a multiverse of independent causal domains, the vacuum energy is another unrelated arbitrary constant, and the same is true of the height of the inflationary plateau present in a huge variety of potentials. Unlike in the conformal equivalent of full general relativity, flat potentials are found to be possible in all spacetime dimensions for polynomial lagrangians of all orders. Hence, we are led to a novel interpretation of the cosmological constant vacuum energy problem and have accelerated inflationary expansion in the very early universe with a very small cosmological constant at late times for a wide range of no-scale theories. Fine-tunings required in traceless general relativity or standard non-traceless f(R) theories of gravity are avoided. We show that the predictions of the scale-invariant conformal potential are completely consistent with microwave background observational data concerning the primordial tilt and the tensor-to-scalar ratio.

On the Hoyle-Narlikar theory of gravitation

1965 ◽  
Vol 286 (1406) ◽  
pp. 313-319 ◽  
Keyword(s):  
Boundary Condition ◽  
Action Principle ◽  
Einstein Equations ◽  
Expanding Universe ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Negative Mass ◽  
The World ◽  
Theory Of Gravitation ◽  
Particle Action

It is shown that the direct-particle action-principle from which Hoyle & Narlikar derive their new theory of gravitation not only yields the Einstein field-equations in the ‘smoothfluid’ approximation, but also implies that the ‘ m ’-field be given by the sum of half the retarded field and half the advanced field calculated from the world-lines of the particles. This is in effect a boundary condition for the Einstein equations, and it appears that it is incompatible with an expanding universe since the advanced field would be infinite. A possible way of overcoming this difficulty would be to allow the existence of negative mass.

Gravitational Field Equations

1971 ◽  
Vol 49 (6) ◽  
pp. 678-684
Author(s):  
Peter Rastall
Keyword(s):  
Gravitational Field ◽  
Einstein Equations ◽  
Tensor Form ◽  
Field Equations ◽  
Scalar Theory ◽  
Gravitational Fields ◽  
Gravitational Field Equations ◽  
Theory Of Gravitation ◽  
Alternative Field

An earlier, scalar theory of gravitation is assumed to be valid for a class of static gravitational fields. The theory is written in tensor form, and generalized to the case of an arbitrary gravitational field. The interaction between the field and its sources is discussed, and the linearized form of the field equations is derived. Some possible alternative field equations are considered which are compatible with the linearized Einstein equations.

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.

Sign in / Sign up

Export Citation Format

Share Document