Behavior of elliptical objects in general theory of relativity

2011 ◽  
Vol 1 (1) ◽  
pp. 1-5
Author(s):  
Bijan Nikouravan ◽  
Keyword(s):  
Gravitational Field ◽  
Line Element ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Spherical Form ◽  
Celestial Object ◽  
Einstein's Field Equations

The simplest solution to Einstein's field equations is the Schwarzschild solution. This solution is not able to describe any non-spherical shaped objects. Some stars and galaxies are ellipsoidal. Consequently, the gravitational field around these objects should be different in comparison with the spherical form. This paper is considering a new line element so that we are able to construct not only spherical objects but also we are able to explain an ellipsoidal object too. This new line element is more accurate and complete than the Schwarzschild line element. In this research, we see that the Schwarzschild line element and its solution is only a part of the whole work, which we have done. For more consideration, we applied this metric to an arbitrary object in the next step. Moreover, we used this line element for the solution of a planetary orbit of an ellipsoid planet by using Einstein’s field equations. These equations used for the exterior solution of an ellipsoidal celestial object.

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.

Proof that Einstein’s field equations are invalid: Exposition of the unimodular defect

2021 ◽  
Vol 34 (4) ◽  
pp. 420-428
Author(s):  
Stephen J. Crothers
Keyword(s):  
Gravitational Field ◽  
Differential Invariant ◽  
Albert Einstein ◽  
Mathematical Foundation ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Field Equations ◽  
First Order ◽  
Gravitational Field Equations ◽  
Pure Mathematics

Albert Einstein first presented his gravitational field equations in unimodular coordinates. In these coordinates, the field equations can be written explicitly in terms of the Einstein pseudotensor for the energy-momentum of the gravitational field. Since this pseudotensor produces, by contraction, a first-order intrinsic differential invariant, it violates the laws of pure mathematics. This is sufficient to prove that Einstein’s unimodular field equations are invalid. Since the unimodular form must hold in the general theory of relativity, it follows that the latter is also physically and mathematically unsound, lacking a proper mathematical foundation.

scholarly journals Eine Welt im Werden

1985 ◽  
Vol 40 (12) ◽  
pp. 1171-1181
Author(s):  
Fritz Bopp
Keyword(s):  
Gravitational Constant ◽  
Line Element ◽  
Big Bang ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Average Value ◽  
Einstein's Field Equations ◽  
The World ◽  
General Relativistic ◽  
The Big Bang

If μ equals the average value of the cosmical density of matter, and if G equals Newton's gravitational constant, the length R = c/√Gμ nearly yields the radius of the world. Therefore it should not be necessary to introduce a second radius K of the same kind as in Einstein's or Friedman's line element ds2 = - gμν( x / K ) dχμ dχν. For this reason, we apply Einstein's field equations on the line element ds2 = dt2 - ∫ (ϱ)2 dr2, ϱ = r/t, c = 1, and obtain a world which is steadily coming to be. The Big-Bang-world is replaced by an expanding one whose mass M is steadily growing according to dM/dt ~ c3/G. It should be taken into account that less assumptions are necessary for a general relativistic world which is coming to be.

scholarly journals Generalization of Vaidya’s Metric for A Radiating Star to Rotating Star

2021 ◽  
Vol 1 (1) ◽  
pp. 1-7
Author(s):  
J.J. Rawal ◽  
◽  
Bijan Nikouravan
Keyword(s):  
Gravitational Field ◽  
External Solution ◽  
Kerr Solution ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Radiating Star ◽  
Rotating Star ◽  
Approximate Version

Schwarzschild's external solution of Einstein’s gravitational field equations in the general theory of relativity for a static star has been generalized by Vaidya [1], taking into account the radiation of the star. Here, we generalize Vaidya’s metric to a star that is rotating and radiating. Although, there is a famous Kerr solution [2] for a rotating star, but here is a simple solution for a rotating star which may be termed as a zero approximate version of the Kerr solution. Results are discussed.

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.

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