On The Motion of Particles in General Relativity Theory

1949 ◽  
Vol 1 (3) ◽  
pp. 209-241 ◽  
Author(s):  
A. Einstein ◽  
L. Infeld
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equations Of Motion ◽  
Relativity Theory ◽  
Fundamental Importance ◽  
Approximation Procedure ◽  
High Approximation ◽  
Field Equations ◽  
General Relativity Theory ◽  
First Time

The gravitational field manifests itself in the motion of bodies. Therefore the problem of determining the motion of such bodies from the field equations alone is of fundamental importance. This problem was solved for the first time some ten years ago and the equations of motion for two particles were then deduced [1]. A more general and simplified version of this problem was given shortly thereafter [2].Mr. Lewison pointed out to us, that from our approximation procedure, it does not follow that the field equations can be solved up to an arbitrarily high approximation. This is indeed true.

The Coordinate Conditions and the Equations of Motion

1953 ◽  
Vol 5 ◽  
pp. 17-25 ◽  
Author(s):  
L. Infeld
Keyword(s):  
General Relativity ◽  
Coordinate System ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Relativity Theory ◽  
Field Equations ◽  
General Relativity Theory ◽  
Coordinate Conditions

The problem of the field equations and the equations of motion in general relativity theory is now sufficiently clarified. The equations of motion can be deduced from pure field equations by treating matter as singularities, [2; 3], or from field equations with the energy momentum tensor [4]. Recently two papers appeared in which the problem of the coordinate system was considered [5; 8]. The two papers are in general agreement as far as the role of the coordinate system is concerned. Yet there are some differences which require clarification.

Radiation and Gravitational Equations of Motion

1951 ◽  
Vol 3 ◽  
pp. 195-207 ◽  
Author(s):  
L. Infeld ◽  
A. E. Scheidegger
Keyword(s):  
General Relativity ◽  
Equations Of Motion ◽  
Classical Field ◽  
Relativity Theory ◽  
Field Theories ◽  
Field Equations ◽  
General Relativity Theory ◽  
Principle Of Superposition ◽  
Classical Field Theories ◽  
Gravitational Equations

Among the classical field theories, general relativity theory occupies a somewhat peculiar place. Unlike those of most other field theories, the field equations in relativity theory are non-linear. This implies that many facts, well known in linear theories, have no analogues in general relativity theory, and conversely. The equations of motion of the sources of the gravitational field are contained in the field equations, a fact which does not apply for the motion of an electron in the electromagnetic field. Conversely, it is difficult to define the notion of a wave (familiar in electrodynamics) in relativity theory; for, the linear principle of superposition is crucial for the existence of waves (at least in the sense that the notion of a wave is normally used).

Modified field equations from a complexified nonlocal metric

2019 ◽  
Vol 97 (8) ◽  
pp. 816-827
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
General Relativity ◽  
Covariant Derivative ◽  
Equations Of Motion ◽  
Space Time ◽  
Relativity Theory ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
General Relativity Theory ◽  
Higher Derivative ◽  
Tangent Vectors

We argue that it is possible to obtain higher-derivative Einstein’s field equations by means of an extended complexified backward–forward nonlocal extension of the space–time metric, which depends on space–time vectors. Our approach generalizes the notion of the covariant derivative along tangent vectors of a given manifold, and accordingly many of the differential geometrical operators and symbols used in general relativity. Equations of motion are derived and a nonlocal complexified general relativity theory is formulated. A number of illustrations are proposed and discussed accordingly.

Red shift of photon frequency in the gravitational field

2021 ◽  
Author(s):  
Jin Tong Wang ◽  
Jiangdi Fan ◽  
Aaron X. Kan
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Gravitational Potential ◽  
Schrodinger Equation ◽  
Red Shift ◽  
Relativity Theory ◽  
Gravitational Redshift ◽  
General Relativity Theory ◽  
Photon Frequency

It has been well known that there is a redshift of photon frequency due to the gravitational potential. Scott et al. [Can. J. Phys. 44 (1966) 1639, https://doi.org/10.1139/p66-137 ] pointed out that general relativity theory predicts the gravitational redshift. However, using the quantum mechanics theory related to the photon Hamiltonian and photon Schrodinger equation, we calculate the redshift due to the gravitational potential. The result is exactly the same as that from the general relativity theory.

Exact solutions of the field equations: twist-free pure radiation fields

1962 ◽  
Vol 270 (1342) ◽  
pp. 328-334 ◽  
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Radiation Field ◽  
Relativity Theory ◽  
Vacuum Field ◽  
Field Equations ◽  
General Relativity Theory ◽  
Pure Radiation ◽  
Radiation Fields ◽  
Null Congruence

This note is intended to give a rough survey of the results obtained in the study of twist-free pure radiation fields in general relativity theory. Here we are using the following Definition. A space-time ( V 4 of signature +2) is called a pure radiation field if it contains a distortion-free geodetic null congruence (a so-called ray congruence ), and if it satisfies certain field equations which we will specify below (e.g. Einstein’s vacuum-field equations). A (null) congruence is called twist-free if it is hypersurface-orthogonal (or ‘normal’). The results listed below were obtained by introducing special (‘canonical’) co-ordinates adapted to the ray congruence. Detailed proofs were given by Robinson & Trautman (1962) and by Jordan, Kundt & Ehlers (1961) (see also Kundt 1961). For the sake of completeness we include in our survey the subclass of expanding fields, and make use of some formulae first obtained by Robinson & Trautman.

VAN DER WAALS FORCES IN CURVED SPACE AS A QUANTUM TOOL TO TEST GENERAL RELATIVITY THEORY

2005 ◽  
Vol 14 (06) ◽  
pp. 995-1008 ◽  
Author(s):  
FABRIZIO PINTO
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Experimental Test ◽  
Point Charge ◽  
Van Der Waals ◽  
Atom Interferometry ◽  
Relativity Theory ◽  
Spherically Symmetric ◽  
General Relativity Theory ◽  
Curved Space

It has been known shortly after the introduction of the general relativity theory that the electrostatic Coulomb potential of a point charge supported in a gravitational field is not spherically symmetric and becomes warped in curved space. Under ordinary laboratory conditions, this effect is quite small and has never been directly observed. Surprisingly, this distortion causes the appearance of a hitherto unknown, topologically complex non-central van der Waals force whose detection is well within range of existing trapped atom interferometry techniques. This will allow for an unexpected experimental test of gravity theory by means of quantum-electro-dynamical interatomic forces.

scholarly journals On Hilbert's world-function

1927 ◽  
Vol 113 (765) ◽  
pp. 496-511 ◽  
Keyword(s):  
Dynamical System ◽  
General Relativity ◽  
Minimum Principle ◽  
Relativity Theory ◽  
Field Equations ◽  
General Relativity Theory ◽  
Least Action ◽  
Principle Of Least Action ◽  
The Universe ◽  
World Function

The well-known theorem that the motion of any conservative dynamical system can be determined from the “Principle of Least Action” or “Hamilton’s Principle” was carried over into General Relativity-Theory in 1915 by Hilbert, who showed that the field-equations of gravitation can be deduced very simply from a minimum-principle. Hilbert generalised his ideas into the assertion that all physical happenings (gravitational electrical, etc.) in the universe are determined by a scalar “world-function” H, being, in fact, such as to annul the variation of the integral ∫∫∫∫H√(−g)dx 0 dx 1 dx 2 dx 3 where ( x 0 , x 1 , x 2 , x 3 ) are the generalised co-ordinates which specify place and time, and g is (in the usual notation of the relativity-theory) the determinant of the gravitational potentials g v q , which specify the metric by means of the equation dx 2 = ∑ p, q g vq dx v dx q . In Hilbert’s work, the variation of the above integral was supposed to be due to small changes in the g vq 's and in the electromagnetic potentials, regarded as functions of x 0 , x 1 , x 2 , x 3 .

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