AN APPROACH TO A THEORY OF GRAVITATION

1960 ◽  
Vol 38 (8) ◽  
pp. 975-982 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
Space Time ◽  
Red Shift ◽  
Additive Constant ◽  
The Sun ◽  
Field Equations ◽  
Scalar Theory ◽  
Theory Of Gravitation ◽  
Bending Of Light

The form of the space–time metric in a scalar theory of gravitation follows from the assumption that the potential is arbitrary to the extent of an additive constant. No field equations are needed. Expressions are found for the gravitational red shift, the perihelion motion of a planet, and the bending of light by the sun. From the observed values of these quantities one can determine the metric and the potential due to a gravitating mass.

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 HIGHER DIMENSIONAL SZEKERES' SPACE–TIME IN BRANS–DICKE SCALAR TENSOR THEORY

2004 ◽  
Vol 13 (06) ◽  
pp. 1073-1083
Author(s):  
ASIT BANERJEE ◽  
UJJAL DEBNATH ◽  
SUBENOY CHAKRABORTY
Keyword(s):  
Turning Point ◽  
Coupling Parameter ◽  
Big Bang ◽  
Space Time ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Tensor Theory ◽  
Higher Dimensional ◽  
Theory Of Gravitation ◽  
The Big Bang

The generalized Szekeres family of solution for quasi-spherical space–time of higher dimensions are obtained in the scalar tensor theory of gravitation. Brans–Dicke field equations expressed in Dicke's revised units are exhaustively solved for all the subfamilies of the said family. A particular group of solutions may also be interpreted as due to the presence of the so-called C-field of Hoyle and Narlikar and for a chosen sign of the coupling parameter. The models show either expansion from a big bang type of singularity or a collapse with the turning point at a lower bound. There is one particular case which starts from the big bang, reaches a maximum and collapses with the in course of time to a crunch.

Experimental tests of a new theory of gravitation

1981 ◽  
Vol 59 (2) ◽  
pp. 283-288 ◽  
Author(s):  
J. W. Moffat
Keyword(s):  
Upper Bound ◽  
Symmetric Solution ◽  
Satellite Orbit ◽  
Experimental Tests ◽  
Spherically Symmetric ◽  
The Sun ◽  
Field Equations ◽  
Spherically Symmetric Solution ◽  
Perihelion Shift ◽  
Theory Of Gravitation

The predictions for the perihelion shift, the deflection of light, and the delay time of a light ray are calculated in the nonsymmetric theory of gravitation. An upper bound for the parameter l (that occurs as a constant of integration in the static, spherically symmetric solution of the field equations) is obtained for the sun for the experimental value of the perihelion shift of Mercury, yielding [Formula: see text]. The upper bound on [Formula: see text] obtained from the Viking spacecraft time-delay experiment is [Formula: see text]. For [Formula: see text], we find that the theory is consistent with the standard relativistic experiments for the solar system. The theory predicts that the perihelion of a satellite could reverse its direction of precession if it orbits close enough to the sun. The results for a highly eccentric satellite orbit are calculated in terms of the value [Formula: see text].

General relativity in terms of a background space

1963 ◽  
Vol 276 (1366) ◽  
pp. 413-417 ◽  
Keyword(s):  
General Relativity ◽  
Euclidean Space ◽  
Test Particle ◽  
Space Time ◽  
Red Shift ◽  
Schwarzschild Metric ◽  
Background Space ◽  
Light Rays ◽  
Theory Of Gravitation

R. d’E. Atkinson has shown that the path of a test particle, the light rays and the gravitational red shift predicted by general relativity for the case of the Schwarzschild metric may all be interpreted in terms of Euclidean space. By introducing the concept of a background space it is shown that Atkinson’s interpretation may be extended for the case of any finite static gravitating system. It is pointed out that the interpretation is applicable to any theory of gravitation in which the path of a test particle and the light rays are geodesics of the space-time metric.

PHOTONS IN THE GRAVITATIONAL FIELD

1966 ◽  
Vol 44 (7) ◽  
pp. 1639-1648 ◽  
Author(s):  
J. C. W. Scott
Keyword(s):  
Quantum Theory ◽  
Gravitational Field ◽  
Group Velocity ◽  
Gravitational Potential ◽  
Rest Mass ◽  
Red Shift ◽  
Field Equations ◽  
Proper Mass ◽  
Photon Frequency ◽  
Theory Of Gravitation

In a previous paper, "The Gravitokinetic Field and the Orbit of Mercury," a new theory of gravitation was introduced, according to which space–time is always flat and the gravitational field is described by equations of Maxwellian form. In this paper it is shown that the theory correctly predicts the gravitational red shift and the gravitational deflection of a light ray. The interaction of photons with a gravitational field follows from the basic premises of quantum theory, that photon frequency is proportional to its energy and that photon wavelength is inversely proportional to its momentum. The photon velocity and proper mass depend on the gravitational potential, and the deflection of a light ray is due to gravitational refraction. The validity of the antisymmetric field equations for sources of variable rest mass is due to the divergence of the group velocity from the dynamical velocity.

Gravitational red shift and time delay of radar echo in f(R)-gravity

2016 ◽  
Vol 13 (04) ◽  
pp. 1650051
Author(s):  
Ying Wang ◽  
Feng He
Keyword(s):  
Time Delay ◽  
Experimental Observation ◽  
Space Time ◽  
Red Shift ◽  
Spectral Lines ◽  
Observation Data ◽  
The Sun ◽  
Schwarzschild Metric ◽  
Radar Echo ◽  
Asymptotic Speed

Sobouti proposes an action-based [Formula: see text] modification of Einstein’s gravity, which admits a similar Schwarzschild metric. A test star moving in such a space–time acquires a constant asymptotic speed at large distances. As we are concerned with two classical tests of Einstein’s theory which are gravitational red shift of spectral lines and time delay of radar echo passing the sun, we shall calculate them in the [Formula: see text]-gravity and show that the results are consistent with the experimental observation data.

Planetary orbits for a moving Sun

1969 ◽  
Vol 47 (20) ◽  
pp. 2161-2164 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
The Sun ◽  
Coordinate Systems ◽  
Scalar Theory ◽  
Planetary Orbits ◽  
Theory Of Gravitation

The scalar theory of gravitation is known to be in agreement with observed planetary motions if the Sun is assumed to be stationary with respect to the preferred coordinate systems of the theory. We now assume that the Sun is moving, and we find that, unless its speed is improbably small, there are observable effects on the planetary orbits. The difficulty can be overcome if one assumes that the Newtonian charts are determined by the distribution of matter.

scholarly journals Axially Symmetric Bulk Viscous String Cosmological Models in GR and Brans-Dicke Theory of Gravitation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
V. U. M. Rao ◽  
D. Neelima
Keyword(s):  
General Relativity ◽  
Bulk Viscosity ◽  
Space Time ◽  
Cosmological Models ◽  
Axially Symmetric ◽  
Matter Distribution ◽  
Field Equations ◽  
Theory Of Gravitation ◽  
The Universe ◽  
Special Case

Axially symmetric string cosmological models with bulk viscosity in Brans-Dicke (1961) and general relativity (GR) have been studied. The field equations have been solved by using the anisotropy feature of the universe in the axially symmetric space-time. Some important features of the models, thus obtained, have been discussed. We noticed that the presence of scalar field does not affect the geometry of the space-time but changes the matter distribution, and as a special case, it is always possible to obtain axially symmetric string cosmological model with bulk viscosity in general relativity.

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.

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