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 Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Zahra Haghani ◽  
Tiberiu Harko
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Newtonian Limit ◽  
Gravity Models ◽  
Momentum Balance ◽  
Field Equations ◽  
Gravitational Fields ◽  
Generalized Poisson

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

scholarly journals Geometrodynamik

1976 ◽  
Vol 31 (10) ◽  
pp. 1155-1159 ◽  
Author(s):  
F. Vollendorf
Keyword(s):  
Gravitational Field ◽  
Maxwell Field ◽  
Field Equations ◽  
Theory Of Gravitation ◽  
Special Case

Abstract This article is based upon the idea to solve the problem of combining the electromagnetic and the gravitational field by starting from Maxwell's theory. It is shown that the theory of the Maxwell field can be generalized in such a way that Einstein's theory of gravitation becomes a special case of it. Finally we find field equations which refer only to geometric quantities.

scholarly journals On electric phenomena in gravitational fields

1927 ◽  
Vol 116 (775) ◽  
pp. 720-735 ◽  
Keyword(s):  
Gravitational Field ◽  
Electromagnetic Waves ◽  
Wave Length ◽  
Gravitational Effect ◽  
Electromagnetic Theory ◽  
Relativity Theory ◽  
Elementary Functions ◽  
Field Equations ◽  
Gravitational Fields ◽  
Particular Solutions

It is a consequence of general relativity that all electromagnetic and optical phenomena are influenced by a gravitational field. Indeed, the first prediction of relativity-theory, namely, the bending of light-rays when they pass near a massive body such as the sun, was a p articular application of this principle. Evidently, therefore, the classical electromagnetic theory must be rewritten in order to take account of the interaction between electromagnetism and gravitation; but beyond laying down general principles, comparatively little progress has been made hitherto in this task, the mathematical difficulties of solving definite electrical problems in a gravitational field being somewhat formidable. The subject is, however, of some interest to atomic physics; for if we assume that the atom has a massive nucleus with electrons in its immediate neighbourhood, the behaviour of such electrons (especially with regard to radiation) will be affected by the gravitational field of the nucleus. In the present paper two kinds of gravitational field are considered, namely, the field due to a single attracting centre ( i, e ., the field whose metric was discovered by Schwarzschild) and a limiting form of it. Within these gravita­tional fields we suppose electromagnetic fields to exist. Strictly speaking, the electromagnetic field has itself a gravitational effect, i.e. , it changes the metric everywhere; but this effect is in general; small, and we shall treat the ideal case in which it is ignored, so we shall suppose the metric to be simply that of the gravitational field originally postulated. The general equations of the electro­magnetic field are obtained, and particular solutions are found, which are the analogues of well-known particular solutions in the classical electromagnetic theory; notably the fields due to electrons at rest, electrostatic fields in general, and spherical electromagnetic waves. The results of the investigation are for the most part expressible only in terms of Bessel functions and certain new functions which are introduced; but in some interesting cases the electro­magnetic phenomena can be represented in term s of elementary functions, as, for instance, the electric field due to an electron in a quasi-uniform gravitational field (equations (15) and (19) below) and the spherical electromagnetic waves of short wave-length about a gravitating centre (equation (43) below).

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.

Spherically symmetric static matter configurations with vanishing radial pressure

2014 ◽  
Vol 24 (01) ◽  
pp. 1550002 ◽  
Author(s):  
S. Thirukkanesh ◽  
M. Govender ◽  
D. B. Lortan
Keyword(s):  
Gravitational Field ◽  
Radial Pressure ◽  
Constant Density ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
New Family ◽  
Generating Method ◽  
Static Solutions ◽  
Special Case

We present a new family of spherically symmetric, static solutions of the Einstein field equations in isotropic, comoving coordinates. The radial pressure at each interior point of these models vanishes yet equilibrium is still possible. The constant density Florides solution which describes the gravitational field inside an Einstein cluster is obtained as a special case of our solution-generating method. We show that our solutions can be utilized to model strange star candidates such as Her. X-1, SAX J1808.4-3658(SS2), SAX J1808.4-3658(SS1) and PSR J1614-2230.

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.

scholarly journals Distribution of phantom dark matter in dwarf spheroidals

2020 ◽  
Vol 640 ◽  
pp. A26 ◽  
Author(s):  
Alistair O. Hodson ◽  
Antonaldo Diaferio ◽  
Luisa Ostorero
Keyword(s):  
Dark Matter ◽  
Gravitational Field ◽  
External Field ◽  
Large Scale ◽  
Milky Way ◽  
Local Group ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Gravitational Fields ◽  
Theory Of Gravity

We derive the distribution of the phantom dark matter in the eight classical dwarf galaxies surrounding the Milky Way, under the assumption that modified Newtonian dynamics (MOND) is the correct theory of gravity. According to their observed shape, we model the dwarfs as axisymmetric systems, rather than spherical systems, as usually assumed. In addition, as required by the assumption of the MOND framework, we realistically include the external gravitational field of the Milky Way and of the large-scale structure beyond the Local Group. For the dwarfs where the external field dominates over the internal gravitational field, the phantom dark matter has, from the star distribution, an offset of ∼0.1−0.2 kpc, depending on the mass-to-light ratio adopted. This offset is a substantial fraction of the dwarf half-mass radius. For Sculptor and Fornax, where the internal and external gravitational fields are comparable, the phantom dark matter distribution appears disturbed with spikes at the locations where the two fields cancel each other; these features have little connection with the distribution of the stars within the dwarfs. Finally, we find that the external field due to the large-scale structure beyond the Local Group has a very minor effect. The features of the phantom dark matter we find represent a genuine prediction of MOND, and could thus falsify this theory of gravity in the version we adopt here if they are not observationally confirmed.

Newtonian quantum gravity and the derivation of the gravitational constant G and its fluctuations

2020 ◽  
Vol 33 (4) ◽  
pp. 387-394
Author(s):  
Reiner Georg Ziefle
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Quantum Physics ◽  
Gravitational Constant ◽  
Dimensional Space ◽  
Wave Theory ◽  
Space Time ◽  
Gravitational Fields ◽  
General Relativistic ◽  
Theory Of Gravity

The theory of gravity “Newtonian quantum gravity” (NQG) is an ingeniously simple theory, because it precisely predicts so-called “general relativistic phenomena,” as, for example, that observed at the binary pulsar PSR B1913 + 16, by just applying Kepler’s second law on quantized gravitational fields. It is an irony of fate that the unsuspecting relativistic physicists still have to effort with the tensor calculations of an imaginary four-dimensional space-time. Everybody can understand that a mass that moves through space must meet more “gravitational quanta” emitted by a certain mass, if it moves faster than if it moves slower or rests against a certain mass, which must cause additional gravitational effects that must be added to the results of Newton's theory of gravity. However, today's physicists cannot recognize this because they are caught in Einstein's relativistic thinking and as general relativity can coincidentally also predict these quantum effects by a mathematically defined four-dimensional curvature of space-time. Advanced NQG is also able to derive the gravitational constant G and explains why G must fluctuate. The “string theory” tries to unify quantum physics with general relativity, but as the so-called “general relativistic” phenomena are quantum physical effects, it cannot be a realistic theory. The “energy wave theory” is lead to absurdity by the author.

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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