Long range forces and broken symmetries

1973 ◽  
Vol 333 (1595) ◽  
pp. 403-418 ◽  
Keyword(s):  
Gravitational Constant ◽  
Equations Of Motion ◽  
Vacuum Field ◽  
Field Equations ◽  
Field Function ◽  
Closed Loops ◽  
Broken Symmetries ◽  
Action Integral ◽  
Theory Of Gravitation ◽  
Set Up

There are reasons for believing that the gravitational constant varies with time. Such a variation would force one to modify Einstein’s theory of gravitation. It is proposed that the modification should consist in the revival of Weyl’s geometry, in which lengths are non-integrable when carried around closed loops, the lack of integrability being connected with the electromagnetic field. A new action principle is set up, much simpler than Weyl’s, but requiring a scalar field function to describe the gravitational field, in addition to the g μν . The vacuum field equations are worked out and also the equations of motion for a particle. An important feature of Weyl’s geometry is that it leads to a breaking of the C and T symmetries, with no breaking of P or of CT . The breaking does not show itself up with the simpler kinds of charged particles, but requires a more complicated kind of term in the action integral for the particle.

The equations of motion in the non-symmetric unified field theory

1954 ◽  
Vol 226 (1166) ◽  
pp. 366-377 ◽  
Keyword(s):  
Equations Of Motion ◽  
Coulomb Force ◽  
Unified Field Theory ◽  
Field Equations ◽  
Original Theory ◽  
Unified Field ◽  
Theory Of Gravitation ◽  
The One ◽  
A Charge ◽  
Weak Fields

The field equations of the non-symmetric unified theory of gravitation and electromagnetism are changed so that they imply the existence of the Coulomb force between electric charges. It is shown that the equations of motion of charged masses then follow correctly to the order of approximation considered. The equations for weak fields in the modified theory are derived and shown to lead to Maxwell’s equations together with a restriction on the current density. This restriction is different from that in the original theory, and in the static, spherically symmetric case permits a charge distribution more likely to correspond to a particle. The failure of the original theory to lead to the equations of motion is related to the structure of the quantities appearing in it, and reasons are given for supposing that no nonsymmetric theory simpler than the one put forward is likely to give these equations in their conventional form.

The Annotated Manuscript

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Equations Of Motion ◽  
Special Theory ◽  
Material Point ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Field Equations ◽  
Theory Of Gravitation

This section presents annotations of the manuscript of Albert Einstein's canonical 1916 paper on the general theory of relativity. It begins with a discussion of the foundation of the general theory of relativity, taking into account Einstein's fundamental considerations on the postulate of relativity, and more specifically why he went beyond the special theory of relativity. It then considers the spacetime continuum, explaining the role of coordinates in the new theory of gravitation. It also describes tensors of the second and higher ranks, multiplication of tensors, the equation of the geodetic line, the formation of tensors by differentiation, equations of motion of a material point in the gravitational field, the general form of the field equations of gravitation, and the laws of conservation in the general case. Finally, the behavior of rods and clocks in the static gravitational field is examined.

Equations of motion in a generalized theory of gravitation

1981 ◽  
Vol 59 (11) ◽  
pp. 1723-1729 ◽  
Author(s):  
R. B. Mann ◽  
J. W. Moffat
Keyword(s):  
World Line ◽  
Equations Of Motion ◽  
Static Solution ◽  
Coupling Constant ◽  
Field Equations ◽  
Complete Space ◽  
Test Particles ◽  
Theory Of Gravitation ◽  
Definition Of ◽  
Universal Coupling

The problem of the motion of test particles is studied in a theory of gravitation based on a nonsymmetric gμν. According to the conservation laws the test particles can follow two kinds of geodesies, depending on the definition of a local inertial frame in the theory. One of these geodesies is nonmaximal and leads to a timelike and null world line complete space when a new parameter l, that occurs as a constant of integration in the spherically symmetric, static solution of the field equations, satisfies [Formula: see text]. In the theory, the parameter [Formula: see text] where N is the number of fermions in a system and a is a new universal coupling constant that satisfies [Formula: see text]. The physical implications of l and the associated conservation law of fermion number is discussed in detail.

Modeling the dynamics of black holes through balanced equations of motion in the null gauge

2019 ◽  
Vol 16 (09) ◽  
pp. 1950131
Author(s):  
Emanuel Gallo ◽  
Osvaldo M. Moreschi
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Field Equation ◽  
General Framework ◽  
Gravitational Constant ◽  
Equations Of Motion ◽  
Field Equations ◽  
Asymptotic Structure ◽  
Strong Connection ◽  
The Past

We develop further the general framework for modeling the dynamics of the motion of black holes, presented in [E. Gallo and O. M. Moreschi, Modeling the dynamics of black holes through balanced equations of motion, Int. J. Geom. Meth. Mod. Phys. 16(3) (2019) 1950034], by employing a convenient null gauge, in general relativity, for the construction of the balanced equations of motion. This null gauge has the property that the asymptotic structure is intimately related to the interior one; in particular there is a strong connection between the field equations and the balanced equations of motion. Our work is very related to what we have called “Robinson–Trautman (RT) geometries” [S. Dain, O. M. Moreschi and R. J. Gleiser, Photon rockets and the Robinson–Trautman geometries, Class. Quantum Grav. 13(5) (1996) 1155–1160] in the past. These geometries are used in the sense of the general framework, we have presented in [E. Gallo and O. M. Moreschi, Modeling the dynamics of black holes through balanced equations of motion, Int. J. Geom. Meth. Mod. Phys. 16(3) (2019) 1950034]. We present the balanced equations of motion in second order of the acceleration. We solve the required components of the field equation at their respective required orders, [Formula: see text] and [Formula: see text], in terms of the gravitational constant. We indicate how this approach can be extended to higher orders.

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.

scholarly journals Static plane-symmetric solution of a scalar-tensor theory of gravitation

1983 ◽  
Vol 24 (3) ◽  
pp. 339-342 ◽  
Author(s):  
D. R. K. Reddy ◽  
V. U. M. Rao
Keyword(s):  
Exact Solution ◽  
Symmetric Solution ◽  
Empty Space ◽  
Vacuum Field ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Tensor Theory ◽  
Theory Of Gravitation ◽  
Static Plane

AbstractVacuum field equations in a scalar-tensor theory of gravitation, proposed by Ross, are obtained with the aid of a static plane-symmetric metric. A closed form exact solution to the field equations in this theory is presented which can be considered as an analogue of Taub's empty space-time in Einstein's theory.

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 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.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

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.

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