3. Energy-momentum pseudotensors of the gravitational field in the general theory of relativity

1984 ◽  
Vol 26 (2) ◽  
pp. 1715-1717
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Theory Of Relativity ◽  
General Theory Of Relativity

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.

scholarly journals New perturbative method for solving the gravitational N-body problem in the general theory of relativity

2015 ◽  
Vol 24 (06) ◽  
pp. 1550039 ◽  
Author(s):  
Slava G. Turyshev ◽  
Viktor T. Toth
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Reference Frame ◽  
Coordinate Transformation ◽  
The Body ◽  
Coordinate Transformations ◽  
Theory Of Relativity ◽  
Body System ◽  
General Theory Of Relativity ◽  
Perturbative Method

We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical N-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using an arbitrary energy–momentum tensor and assumed to possess any number of internal multipole moments. The solution of the gravitational field equations in any reference frame is presented as a sum of three terms: (i) The inertial flat spacetime in that frame, (ii) unperturbed solutions for each body in the system that is covariantly transformed to the coordinates of this frame and (iii) the gravitational interaction term. We use the harmonic gauge conditions that allow reconstruction of a significant part of the structure of the post-Galilean coordinate transformation functions relating global coordinates of the inertial reference frame to the local coordinates of the noninertial frame associated with a particular body. The remaining parts of these functions are determined from dynamical conditions, obtained by constructing the relativistic proper reference frame associated with a particular body. In this frame, the effect of external forces acting on the body is balanced by the fictitious frame-reaction force that is needed to keep the body at rest with respect to the frame, conserving its relativistic three-momentum. We find that this is sufficient to determine explicitly all the terms of the coordinate transformation. The same method is then used to develop the inverse transformations. The resulting post-Galilean coordinate transformations have an approximate group structure that extends the Poincaré group of global transformations to the case of accelerating observers in a gravitational field of N-body system. We present and discuss the structure of the metric tensors corresponding to the reference frames involved, the rules for transforming relativistic gravitational potentials, the coordinate transformations between frames and the resulting relativistic equations of motion.

scholarly journals Absence of Singularity in Schwarzschild Metric in the Vector Model for Gravitational Field

2012 ◽  
Vol 18 (3) ◽  
pp. 175-184
Author(s):  
Vo Van On
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
General Theory ◽  
Space Time ◽  
Symmetric Body ◽  
Vector Model ◽  
Spherically Symmetric ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Schwarzschild Metric

In this paper, based on the vector model for gravitational field we deduce an equation to determinate the metric of space-time. This equation is similar to equation of Einstein. The metric of space-time outside a static spherically symmetric body is also determined. It gives a small supplementation to the Schwarzschild metric in General theory of relativity but the singularity does not exist. Especially, this model predicts the existence of a new universal body after a black hole.

scholarly journals ON THE SPECTRAL SHIFT AND THE TIME DELAY OF LIGHT IN A RINDLER ACCELERATED FRAME

2007 ◽  
Vol 16 (04) ◽  
pp. 699-709 ◽  
Author(s):  
J. B. FORMIGA ◽  
C. ROMERO
Keyword(s):  
Gravitational Field ◽  
Time Delay ◽  
General Theory ◽  
Equivalence Principle ◽  
Spectral Shift ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Accelerated Observers ◽  
Einstein's Equivalence Principle

We discuss two effects predicted by the general theory of relativity in the context of Rindler accelerated observers: the gravitational spectral shift and the time delay of light. We show that these effects also appear in a Rindler frame in the absence of gravitational field, in accordance with the Einstein's equivalence principle.

scholarly journals Gravitational Waves in Newton’s Gravitation and Criticism of Gravitational Waves Resulting from the General Theory of Relativity (LIGO)

2019 ◽  
Author(s):  
Roman Szostek ◽  
Paweł Góralski ◽  
Kamil Szostek
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Laser Interferometer ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Important Conclusion ◽  
Wave Measurement ◽  
Erroneous Interpretation

The most important conclusion from this article is that from the General Theory of Relativity (GTR) do not result any gravitational waves, but just ordinary modulation of the gravitational field intensities caused by rotating of bodies. If the LIGO team has measured anything, it is only this modulation, rather than the gravitational wave understood as the carrier of gravity. This discussion shows that using too complicated mathematics in physics leads to erroneous interpretation of results (in this case, perhaps the tensor analysis is guilty). Formally, various things can be calculated, but without knowing what such analysis means, they can be attributed misinterpreted. Since the modulation of gravitational field intensities has been called a gravitational wave in contemporary physics, we have also done so, although it is misleading. In the article it was shown, that from the Newton’s law of gravitation resulted an existence of gravitational waves very similar to these, which result from the General Theory of Relativity. The article shows differences between the course of gravitational waves that result from Newton’s gravitation, and the course of gravitational waves that result from the General Theory of Relativity, which measurement was announced by the LIGO (Laser Interferometer Gravitational-Wave Observatory) [1], [2], and [5]. According to both theories, gravitational waves are cyclical changes of the gravitational field intensities. The article proposes a method of testing a laser interferometer for gravitational wave measurement used in the LIGO Observatory. Criticism of results published by the LIGO team was also presented.

scholarly journals A NON- STATIC COSMOLOGICAL MODEL IN THE VECTOR MODEL FOR GRAVITATIONAL FIELD

2011 ◽  
Vol 14 (1) ◽  
pp. 78-84
Author(s):  
On Van Vo
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Cosmological Model ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Vector Model ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
S Model

In this paper, based on the vector model for gravitational field we obtained the modified Friedman equations, which were similar to the classical Friedman equations but were added a term of energy – momentum tensor of gravitational field. Non- static flat cosmological model in this model was similar to General Theory of Relativity (GTR) ‘s model but the expansive rate in the vacuum age was difference with General Theory of Relativity ’s model.

General Covariance

2021 ◽  
pp. 164-210
Author(s):  
Moataz H. Emam
Keyword(s):  
Black Holes ◽  
Gravitational Field ◽  
General Theory ◽  
Weak Field ◽  
General Covariance ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Spacetime Curvature ◽  
Interior Solutions

The general theory of relativity is introduced based on the principle of equivalence. Gravity is shown to arise dues to spacetime curvature. Specific examples of curved spacetimes are presented from the approximate but more intuitive to the complex: Uniform gravitational field (Galilean metric), the Newtonian weak field metric, Schwarzschild’s exterior and interior solutions, black holes, and cosmological spacetimes. A brief discussion on distances, areas and volumes in curved spaces is also given.

On “Belated Decision in the Hilbert-Einstein Priority Dispute”, published by L. Corry, J. Renn, and J. Stachel

2004 ◽  
Vol 59 (10) ◽  
pp. 715-719 ◽  
Author(s):  
F. Winterberg
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Historical Record ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Field Equations ◽  
Probative Value ◽  
Gravitational Field Equations ◽  
Correct Form ◽  
Crucial Part

In a paper, published in 1997 by L. Corry, J. Renn, and J. Stachel, it is claimed that the recently discovered printer’s proofs of Hilbert’s 1915 paper on the general theory of relativity prove that Hilbert did not anticipate Einstein in arriving at the correct form of the gravitational field equations, as it is widely believed, but that only after having seen Einstein’s final paper did Hilbert amend his published version with the correct form of the gravitational field equations. However, because a crucial part of the printer’s proofs of Hilbert’s paper had been cut off by someone, a fact not mentioned in the paper by Corry, Renn, and Stachel, the conclusion drawn by Corry, Renn, and Stachel is untenable and has no probative value. I rather will show that the cut off part of the proofs suggests a crude attempt by some unknown individual to falsify the historical record.

Sign in / Sign up

Export Citation Format

Share Document