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.

Conservation laws and gravitational radiation

1977 ◽  
Vol 55 (15) ◽  
pp. 1342-1348 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
Conservation Laws ◽  
Gravitational Waves ◽  
Gravitational Radiation ◽  
Lagrangian Density ◽  
Total Stress ◽  
Field Equations ◽  
Gravitational Fields ◽  
Previous Version ◽  
Newtonian Approximation

A total stress-momentum is defined for gravitational fields and their sources. The Lagrangian density is slightly different from that in the previous version of the theory, and the field equations are considerably simplified. The post-Newtonian approximation of the theory is unchanged. The existence and nature of weak gravitational waves are discussed.

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.

Post-Newtonian approximation of a new theory of gravity

1981 ◽  
Vol 59 (11) ◽  
pp. 1592-1608 ◽  
Author(s):  
R. B. Mann ◽  
J. W. Moffat
Keyword(s):  
Equations Of Motion ◽  
Multipole Expansion ◽  
Momentum Conservation ◽  
Momentum Tensor ◽  
Newtonian Theory ◽  
Perihelion Precession ◽  
Motion Energy ◽  
Newtonian Approximation ◽  
Theory Of Gravity ◽  
Ppn Parameters

The post-Newtonian approximation is developed for a new theory of gravity based on a Hermitian metric gμν. The approximation gives Newtonian theory in lowest order, but differs from general relativity in post-Newtonian order. The equations of motion, energy–momentum conservation, and perihelion precession are investigated. The equations of motion are derivable from the conservation laws of the energy–momentum tensor. A multipole expansion of the metric is formulated, and the PPN parameters α, β, and γ are found all to be unity. Several new parameters occur, most notably I, which is related to the number density of fermions of a system.

scholarly journals Motion of the relativistic center of mass of the two-body system in the environment

2019 ◽  
Vol 55 (1) ◽  
pp. 77-82
Author(s):  
A. P. Ryabushko ◽  
I. T. Nemanova ◽  
T. A. Zhur
Keyword(s):  
Coordinate System ◽  
Center Of Mass ◽  
Approximation Procedure ◽  
Constant Density ◽  
Theory Of Relativity ◽  
Body System ◽  
Field Equations ◽  
Newtonian Theory ◽  
Newtonian Approximation ◽  
Two Bodies

The motion equations for a system of two bodies moving in a medium are derived in the Cartesian coordinate system in the Newtonian theory. The coordinate system is barycentric, that is, the center of mass of the two-body system is immobile. Using the Einstein – Infeld approximation procedure, the gravitational field created by the “two bodies – medium” system was found from the Einstein field equations, and then the equations of motion of the bodies in this field were obtained.It is shown that in the post-Newtonian approximation of the general theory of relativity, the center of mass of two bodies moving in a gas – dust rarefied medium of constant density, determined by analogy with the Newtonian center of mass, is displaced along the cycloid, although in the Newtonian approximation it is stationary, i.e. the movement along the cycloid occurs with respect to the barycentric Newtonian fixed reference frame. Numerical estimates are given for the magnitude of this displacement. Given a popular value of the medium density ρ = 10–21 g·cm–3 its order can reach 106 km per one rotation of two bodies around their center of mass. In the case of the equality of masses of the bodies, their relativistic center of mass, like their Newtonian center of mass, is immobile.It has been hypothesized that for any elliptical orbits of two bodies and an inhomogeneous distribution of the gas – dust medium the qualitative picture of motion of the relativistic center of mass of the two bodies will not change.

scholarly journals CLASSICAL TRACE ANOMALY

2005 ◽  
Vol 14 (07) ◽  
pp. 1233-1250 ◽  
Author(s):  
M. FARHOUDI
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Second Order ◽  
Alternative Form ◽  
Mathematical Form ◽  
Einstein’S Field Equations ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Trace Anomaly

We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy–momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.

A brief survey of general relativity

2019 ◽  
pp. 25-50
Author(s):  
Nils Andersson
Keyword(s):  
General Relativity ◽  
Geometric Theory ◽  
Einstein’S Field Equations ◽  
Curved Spacetime ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Theory Of Gravity

This chapter provides an overview of Einstein’s geometric theory of gravity – general relativity. It introduces the mathematics required to model the motion of objects in a curved spacetime and provides an intuitive derivation of Einstein’s field equations.

scholarly journals Non-Riemannian description of Robinson–Trautman spacetimes in Brans–Dicke theory of gravity

2019 ◽  
Vol 28 (04) ◽  
pp. 1950070
Author(s):  
Muzaffer Adak ◽  
Tekin Dereli ◽  
Yorgo Şenikoğlu
Keyword(s):  
Scalar Field ◽  
Differential Forms ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Exterior Differential ◽  
Tensor Theory ◽  
Theory Of Gravitation ◽  
Theory Of Gravity ◽  
Future Reference

The variational field equations of Brans–Dicke scalar-tensor theory of gravitation are given in a non-Riemannian setting in the language of exterior differential forms over four-dimensional spacetimes. A conformally rescaled Robinson–Trautman metric together with the Brans–Dicke scalar field are used to characterize algebraically special Robinson–Trautman spacetimes. All the relevant tensors are worked out in a complex null basis and given explicitly in an appendix for future reference. Some special families of solutions are also given and discussed.

Kerr–Newman solution in modified teleparallel theory of gravity

2014 ◽  
Vol 24 (01) ◽  
pp. 1550007 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Azimuthal Angle ◽  
Polar Angle ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Square Root ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Teleparallel Theory ◽  
Theory Of Gravity

A nondiagonal tetrad field having six unknown functions plus an angle Φ, which is a function of the radial coordinate r, azimuthal angle θ and the polar angle ϕ, is applied to the charged field equations of modified teleparallel theory of gravity. A special nonvacuum solution is derived with three constants of integration. The tetrad field of this solution is axially symmetric and its scalar torsion is constant. The associated metric of the derived solution gives Kerr–Newman spacetime. We have shown that the derived solution can be described by a local Lorentz transformations plus a diagonal tetrad field that is the square root of the Kerr–Newman metric. We show that any solution of general relativity (GR) can be a solution in f(T) under certain conditions.

The contraction of gravitating spheres

1964 ◽  
Vol 281 (1384) ◽  
pp. 39-48 ◽  
Keyword(s):  
General Relativity ◽  
Constant Density ◽  
Field Equations ◽  
Newtonian Theory ◽  
Full Field ◽  
Invariant Integral ◽  
Density Relation ◽  
Particle Paths ◽  
Rigorous Method ◽  
Adiabatic Contraction

Earlier ideas associating an invariant integral of the energy invariant with the number of nucleons in a gravitating body are shown to be fallacious, and thus do not provide a means of following through the contraction of such a body. It is shown how the full field equations of general relativity give a feasible and rigorous method of examining contracting models. Schwarzschild-type co-ordinates are introduced and are used to examine the slow adiabatic contraction of a sphere of constant density. The particle paths are found and the pressure-density relation permitting such slow adiabatic contraction is examined. It is shown that the simple 4/3 power law of Newtonian theory has to be replaced by a steeper dependence of pressure on density for high gravitational potentials. Radiation co-ordinates are introduced to examine radiating contracting systems, and equations fully specifying such a system are obtained. A simple example is given in outline to illustrate the method.

scholarly journals ON THE GRAVITATIONAL ENERGY–MOMENTUM VECTOR IN f(T) THEORIES

2013 ◽  
Vol 22 (10) ◽  
pp. 1350069 ◽  
Author(s):  
S. C. ULHOA ◽  
E. P. SPANIOL
Keyword(s):  
General Expression ◽  
Lagrangian Density ◽  
Functional Form ◽  
Gravitational Energy ◽  
Closed Universe ◽  
Field Equations ◽  
Momentum Vector ◽  
Open Universe

This work is devoted to present and analyze an expression for the gravitational energy–momentum vector in the context of f(T) theories through field equations. Such theories are the analogous counterpart of the well-known f(R) theories, except using torsion instead of curvature. We obtain a general expression for the gravitational energy–momentum vector in this framework. Using the hypothesis of the isotropy of spacetime, we find the gravitational energy for a closed universe, since construction of real tetrads that do not constrain the functional form of the Lagrangian density was not possible for an open universe. Thus, we find a vanishing gravitational energy for the tetrad that we have used.

Sign in / Sign up

Export Citation Format

Share Document