The Newtonian theory of gravitation and its generalization

1979 ◽  
Vol 57 (7) ◽  
pp. 944-973 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
Complete Theory ◽  
Newtonian Theory ◽  
Gravitational Fields ◽  
Newtonian Approximation ◽  
Geometrical Form ◽  
Theory Of Gravitation ◽  
Two Stages ◽  
Relativistic Gravitation

The classical, Newtonian theory of gravitation is generalized in two stages. First, a theory is constructed which is valid for a class of strong, static gravitational fields. This theory, which we call the newtonian theory, is compatible with all the classical tests of relativistic gravitation. The newtonian theory is then rewritten in a covariant, geometrical form and is generalized to give a complete theory of gravitation whose post-Newtonian approximation is in agreement with all observations.

A theory of gravity

1976 ◽  
Vol 54 (1) ◽  
pp. 66-75 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
Gravitational Field ◽  
Gravitational Constant ◽  
Complete Theory ◽  
Field Equations ◽  
Newtonian Theory ◽  
Gravitational Fields ◽  
Slight Generalization ◽  
Solar Oblateness ◽  
Theory Of Gravity ◽  
Special Case

It is known that a slight generalization of the Newtonian theory of gravity is compatible with all present-day observations. This 'super-Newtonian' theory is not a complete theory of gravity, since it applies only to static or quasistatic gravitational fields. We develop here a simple, complete theory of gravity that contains the super-Newtonian theory as a special case. The gravitational field is described in terms of two real functions, and the field equations are derived from a variational principle. The homogeneous cosmological solutions of the field equations all correspond to open universes. The gravitational 'constant' decreases with time in the version of the theory that is compatible with Dicke's measurement of the solar oblateness, but not in the version compatible with an almost spherical Sun. The gravitational field of a slowly rotating body is not of the Lense-Thirring form.

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.

scholarly journals Astronomical tests of relativity: beyond parameterized post-Newtonian formalism (PPN), to testing fundamental principles

2009 ◽  
Vol 5 (S261) ◽  
pp. 56-61 ◽  
Author(s):  
Vladik Kreinovich
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Final Theory ◽  
Gravitational Theories ◽  
Cosmological Observations ◽  
Partial Analysis ◽  
Theory Of Gravitation ◽  
Improved Accuracy ◽  
Fundamental Physical ◽  
Relativistic Gravitation

AbstractBy the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. This does not mean that General Relativity is the final theory of gravitation: it needs to be reconciled with quantum physics (into quantum gravity), it may also need to be reconciled with numerous surprising cosmological observations, etc. It is, therefore, reasonable to prepare an extended version of the PPN formalism, that will enable us to test possible quantum-related modifications of General Relativity.In particular, we need to include the possibility of violating fundamental principles that underlie the PPN formalism but that may be violated in quantum physics, such as scale-invariance, T-invariance, P-invariance, energy conservation, spatial isotropy violations, etc. In this paper, we present the first attempt to design the corresponding extended PPN formalism, with the (partial) analysis of the relation between the corresponding fundamental physical principles.

scholarly journals Gravitational major-axis contraction of Mercury’s elliptical orbit

2019 ◽  
Vol 34 (20) ◽  
pp. 1950159
Author(s):  
Q. H. Liu ◽  
Q. Li ◽  
T. G. Liu ◽  
X. Wang
Keyword(s):  
Major Axis ◽  
Distance Measurement ◽  
Elliptical Orbit ◽  
Measurement Technology ◽  
The Sun ◽  
Local Curvature ◽  
Newtonian Theory ◽  
Perihelion Precession ◽  
Theory Of Gravitation

The local curvature of the space produced by the Sun causes not only the perihelion precession of Mercury’s elliptical orbit, but also the variations of the whole orbit, in comparison with those predicted by the Newtonian theory of gravitation. Calculations show that the gravitational major-axis contraction of Mercury’s elliptical orbit is 1.3 km which can in principle be confirmed by the present astronomical distance measurement technology.

A note on a theory of gravity

1977 ◽  
Vol 55 (1) ◽  
pp. 38-42 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
Lagrangian Density ◽  
Mathematical Form ◽  
Field Equations ◽  
Newtonian Theory ◽  
Newtonian Approximation ◽  
Theory Of Gravity

An error in a previously published theory of gravity is corrected. Field equations are derived from a Lagrangian density of simple mathematical form. The post-Newtonian approximation is calculated, and the theory is shown to be in agreement with all local observations. The limitations of the standard, parameterized post-Newtonian theory are noted.

Gravitation and cosmic expansion in conformal space-time

1953 ◽  
Vol 49 (2) ◽  
pp. 285-291 ◽  
Author(s):  
Feza Gürsey ◽  
H. Bondi
Keyword(s):  
Steady State ◽  
Scalar Function ◽  
Space Time ◽  
Conformal Space ◽  
Newtonian Theory ◽  
Cosmic Expansion ◽  
Tensor Theory ◽  
Cosmological Problem ◽  
Theory Of Gravitation ◽  
State Universe

AbstractA simple theory of gravitation is formulated in conformal Riemannian space-time. The metric is determined by a scalar function which satisfies a linear equation. A conclusion in favour of Einstein's general tensor theory is drawn from a discussion of the corrections to the Newtonian theory for purely gravitational phenomena. Finally the theory is applied to the cosmological problem and especially to the possibility of a steady-state universe. The velocity-distance law is shown to be compatible with a constant uniform distribution of matter without the need of artificial assumptions.

Neutron configurations in the generalized Newtonian theory of gravitation

Astrophysics ◽  
1968 ◽  
Vol 4 (2) ◽  
pp. 62-67 ◽  
Author(s):  
G. S. Saakyan ◽  
M. A. Mnatsakanyan
Keyword(s):  
Newtonian Theory ◽  
Theory Of Gravitation

scholarly journals THEORY OF GRAVITATION THEORIES: A NO-PROGRESS REPORT

2008 ◽  
Vol 17 (03n04) ◽  
pp. 399-423 ◽  
Author(s):  
THOMAS P. SOTIRIOU ◽  
STEFANO LIBERATI ◽  
VALERIO FARAONI
Keyword(s):  
Equivalence Principle ◽  
Progress Report ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Gravitational Fields ◽  
Stress Energy ◽  
Theories Of Gravity ◽  
Theory Of Gravitation ◽  
Conformal Frames ◽  
Shaky Ground

Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore, interesting enough to deserve further investigation. From this perspective, an alternative title of this paper could be "Why Are We Still Unable to Write a Guide on How to Propose Viable Alternatives to General Relativity?". Attempting to answer this question, it is argued here that earlier efforts to turn qualitative statements, such as the Einstein equivalence principle, into quantitative ones, such as the metric postulates, stand on rather shaky ground — probably contrary to popular belief — as they appear to depend strongly on particular representations of the theory. This includes ambiguities in the identification of matter and gravitational fields, dependence of frequently used definitions (such as those of the stress–energy tensor or classical vacuum) on the choice of variables, etc. Various examples are discussed and possible approaches to this problem are pointed out. In the course of this study, several common misconceptions related to the various forms of the equivalence principle, the use of conformal frames and equivalence between theories are clarified.

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