Physical explanations of Einstein's gravity (original) (raw)
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Einstein's General Theory Of Relativity
2007
I. Introduction: Newtonian Physics and Special Relativity- 1. Relativity Principals and Gravitation 2. The Special Theory of Relativity II. The Mathematics of the General Theory of Relativity- 3. Vectors, Tensors, and Forms 4. Basis Vector Fields and Metric Tensor 5. Non-inertial Reference Frames 6. Differentiation, Connections and Integration 7. Curvature II. Einstein's Field Equations- 8. Einstein's Field Equations 9. The Linear Field Approximation 10. The Schwarzschild Solution and Black Holes IV. Cosmology- 11. Homogeneous and Isotropic Universe Models 12. Universe Models with Vacuum Energy 13. An Anisotropic Universe V. Advanced Topics- 14. Covariant decomposition, Singularities, and Canonical Cosmology 15. Homogeneous Spaces 16. Israel's Formalism: The metric junction method 17. Brane-worlds 18. Kaluza-Klein Theory VI. Appendices- A. Constrants of Nature B. Penrose diagrams C. Anti-de Sitter spacetime D. Suggested further reading
Electrodynamics, 2016
The General Theory of Relativity The general theory of relativity, Einstein's theory of gravitation, has been included as a compulsory subject in undergraduate and graduate courses in Physics and Applied Mathematics all over the world. However, the physics-first approach that is taken by many textbooks is not universally used, as the approach often depends on the instructors' or students' background. Conceived from the lecture notes made by the author over a teaching career spanning 18 years, this book introduces the general theory of relativity for advanced students with a strong mathematical background. The proposed book takes a 'math-first approach', for which the mathematical formalism comes first and is then applied to physics. It presents a concise yet comprehensive and structured understanding of the general theory of relativity. The book discusses the mathematical foundation of the general theory of relativity and focuses heavily on topics such as tensor calculus, geodesics, Einstein field equations, linearized gravity, Lie derivatives and their applications, the causal structure of spacetime, rotating black holes, and basic knowledge of cosmology and astrophysics. All of these are explained through a large number of worked examples and exercises.
Editorial introduction to the special issue "The Renaissance of Einstein’s Theory of Gravitation".
European Physical Journal H, 2017
Einstein’s 1915 theory of gravitation, also known as General Relativity, is now considered one of the pillars of modern physics. It contributes to our understanding of cosmology and of fundamental interactions between particles. But that was not always the case. Between the mid-1920s and the mid-1950s, General Relativity underwent a period of stagnation, during which the theory was mostly considered as a stepping-stone for a superior theory. In a special issue of EPJ H just published, historians of science and physicists actively working on General Relativity and closely related fields share their views on the process, during the post-World War II era, in particular, which saw the “Renaissance” of General Relativity, following progressive transformation of the theory into a bona fidae physics theory. In this special issue, new insights into the historical process leading to this renaissance point to the extension of the foundation of the original theory, ultimately leading to a global transformation in its character. Contributions from several experts reveals that the theory of 1915 was insufficient to reach firm conclusions without being complemented by intuitions drawn from the resources of pre-relativistic physics. Or, in the case of cosmology, the theory needed to be complemented by philosophical considerations that were hardly generalizable to help solve more mundane problems. As physicist Pascual Jordan puts it, there was a “mismatch between the simplicity of the physical and epistemological foundations and the annoying complexity of the corresponding thicket of formulae.” A number of contributions in this special issue also explain how the theory underwent a period of successive controversies, leading by the 1960s, to the renaissance of the theory. Subsequently, it became in the 1970s, an important, empirically well-tested branch of theoretical physics related to the new, successful sub-discipline of relativistic astrophysics.
Einstein's Space-Time An Introduction to Special and General Relativity
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Of pots and holes: Einstein's bumpy road to general relativity
Annalen der Physik, 2005
General relativity in the Annalen and elsewhere Readers of this volume will notice that it contains only a few papers on general relativity. This is because most papers documenting the genesis and early development of general relativity were not published in Annalen der Physik. After Einstein took up his new prestigious position at the Prussian Academy of Sciences in the spring of 1914, the Sitzungsberichte of the Berlin academy almost by default became the main outlet for his scientific production. Two of the more important papers on general relativity, however, did find their way into the pages of the Annalen [35,41]. Although I shall discuss both papers in this essay, the main focus will be on [35], the first systematic exposition of general relativity, submitted in March 1916 and published in May of that year. Einstein's first paper on a metric theory of gravity, co-authored with his mathematician friend Marcel Grossmann, was published as a separatum in early 1913 and was reprinted the following year in Zeitschrift für Mathematik und Physik [50, 51]. Their second (and last) joint paper on the theory also appeared in this journal [52]. Most of the formalism of general relativity as we know it today was already in place in this Einstein-Grossmann theory. Still missing were the generally-covariant Einstein field equations. As is clear from research notes on gravitation from the winter of 1912-1913 preserved in the so-called "Zurich Notebook," 1 Einstein had considered candidate field equations of broad if not general covariance, but had found all such candidates wanting on physical grounds. In the end he had settled on equations constructed specifically to be compatible with energy-momentum conservation and with Newtonian theory in the limit of weak static fields, even though it remained unclear whether these equations would be invariant under any non-linear transformations. In view of this uncertainty, Einstein and Grossmann chose a fairly modest title for their paper: "Outline ("Entwurf") of a Generalized Theory of Relativity and of a Theory of Gravitation." The Einstein-Grossmann theory and its fields equations are therefore also known as the "Entwurf" theory and the "Entwurf" field equations. Much of Einstein's subsequent work on the "Entwurf" theory went into clarifying the covariance properties of its field equations. By the following year he had convinced himself of three things. First, generallycovariant field equations are physically inadmissible since they cannot determine the metric field uniquely. This was the upshot of the so-called "hole argument" ("Lochbetrachtung") first published in an appendix to [51]. 2 Second, the class of transformations leaving the "Entwurf" field equations invariant was as broad
A critical analysis of Schwarzschild-like metrics
2019
By neglecting the cosmological constant Λ, Einstein's field equations in absence of matter and other fields read G ik = 0, which is not reasonable, since it violates the conservation law of total energy, momentum, and stress, because the gravitational field energy and momentum density cannot be represented by a vanishing Einstein tensor. In order to remedy this shortcoming, we construct a uniform metric, which allows us later to get a more general one, that is asymptotically equal to the Schwarzschild metric. This metric has a plausible energy-momentum density tensor of the gravitational field and correctly describes the effect of light deflection, but the perihelion shift of Mercury is overestimated. Because of the authors' different view in order to overcome the shortcomings, different solutions are obtained.
On Theoretical Contradictions and Physical Misconceptions in the General Theory of Relativity
2008
It is demonstrated herein that:-1. The quantity 'r' appearing in the so-called "Schwarzschild solution" is neither a distance nor a geodesic radius in the manifold but is in fact the inverse square root of the Gaussian curvature of the spatial section and does not generally determine the geodesic radial distance (the proper radius) from the arbitrary point at the centre of the spherically symmetric metric manifold. 2. The Theory of Relativity forbids the existence of point-mass singularities because they imply infinite energies (or equivalently, that a material body can acquire the speed of light in vacuo); 3. Ric = R µν = 0 violates Einstein's 'Principle of Equivalence' and so does not describe Einstein's gravitational field; 4. Einstein's conceptions of the conservation and localisation of gravitational energy are invalid; 5. The concepts of black holes and their interactions are ill-conceived; 6. The FRW line-element actually implies an open, infinite Universe in both time and space, thereby invalidating the Big Bang cosmology.
Einstein's hypothesis is confirmed by the example of the Schwarzschild problem
2019
The Newtonian gravity law was deduced with a correction for a non-zero density of a gravity field. The new gravity law is virtually almost entirely congruent with the Schwarzschild attraction law in a zone somewhat distant from the Schwarzschild radius. This confirms with great certainty the hypothesis of A. Einstein that the energy of the gravitational field contributes to the gravitational field. In addition, this contribution is of the same order as the contribution of the Schwarzschild solution. This leads to the conclusion that the energy of the gravitational field should play a large role in the general theory of relativity.
Everything About Einstein’s Relativity Theory
viXra, 2016
This research paper discusses the validity of Einstein’s relativity theory. It took four years of intensive work to reach the final conclusions. All assumptions of Einstein and his mathematics (where it exists) will be reviewed. Experiments done to show the validity will be restudied then we shall show their correctness under the constraints and conditions made by Einstein and show their practical and scientific value. We shall also show how much is the truthfulness of general relativity.