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Journal articles on the topic 'Einstein general relativity'

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Published: 10 March 2023

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1

Barukčić, Ilija. "Anti Einstein – Refutation of Einstein’s General Theory of Relativity." International Journal of Applied Physics and Mathematics 5, no. 1 (2015): 18–28. http://dx.doi.org/10.17706/ijapm.2015.5.1.18-28.

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2

Lo, C. Y. "The Development of Relativity and Einstein." JOURNAL OF ADVANCES IN PHYSICS 10, no. 3 (October 6, 2015): 2874–85. http://dx.doi.org/10.24297/jap.v10i3.1327.

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There are errors in general relativity that must be rectified. As Zhou pointed out, Einstein’s covariance principle is proven to be invalid by explicit examples. Linearization is conditionally valid. Pauli's version of the equivalence principle is impossible in mathematics. Einstein's adaptation of the distance in Riemannian geometry is invalid in physics as pointed out by Whitehead. Moreover, it is inconsistent with the calculation on the bending of light, for which a Euclidean-like framework is necessary. Thus, the interpretation of the Hubble redshifts as due to receding velocities of stars is invalid. The Einstein equation has no dynamic solutions just as Gullstrand suspected. All claims on the existence of dynamic solutions for the Einstein equation are due to mistakes in non-linear mathematics. For the existence of a dynamic solution, the Einstein equation must be modified to the Lorentz-Levy-Einstein equation that have additionally a gravitational energy-stress tensor with an anti-gravity coupling. The existence of photons is a consequence of general relativity. Thus, the space-time singularity theorems of Hawking and Penrose are actually irrelevant to physics because their energy conditions cannot be satisfied. The positive mass theorem of Schoen and Yau is misleading because invalid implicit assumptions are used as Hawking and Penrose did. There are three experiments that show formula E = mc2 is invalid, and a piece of heated-up metal has reduced weight just as a charged capacitor. Thus, the weight is temperature dependent. It is found, due to the repulsive charge-mass interaction, gravity is not always attractive to mass. Since the assumption that gravity is always attractive to mass is not valid, the existence of black holes are questionable. Because of the repulsive charge-mass interaction, the theoretical framework of general relativity must be extended to a five-dimensional relativity of Lo, Goldstein & Napier. Thus Einstein's conjecture of unification is valid. Moreover, the repulsive gravitational force from a charged capacitor is incompatible with the notion of a four-dimensional space. In Quantum theory, currently the charge-mass interaction is neglected. Thus, quantum theory is not a final theory as Einstein claims.
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3

Heller, Michael. "Einstein algebras and general relativity." International Journal of Theoretical Physics 31, no. 2 (February 1992): 277–88. http://dx.doi.org/10.1007/bf00673258.

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4

Heller, Michael, Tomasz Miller, Leszek Pysiak, and Wiesław Sasin. "Generalized derivations and general relativity." Canadian Journal of Physics 91, no. 10 (October 2013): 757–63. http://dx.doi.org/10.1139/cjp-2013-0186.

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We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra [Formula: see text]. Such a derivation, introduced by Brešar in 1991, is given by a linear mapping [Formula: see text] such that there exists a usual derivation, d, of [Formula: see text] satisfying the generalized Leibniz rule u(ab) = u(a)b + ad(b) for all [Formula: see text]. The generalized geometry “is tested” in the case of the algebra of smooth functions on a manifold. We then apply this machinery to study generalized general relativity. We define the Einstein–Hilbert action and deduce from it Einstein’s field equations. We show that for a special class of metrics containing, besides the usual metric components, only one nonzero term, the action reduces to the O’Hanlon action that is the Brans–Dicke action with potential and with the parameter ω equal to zero. We also show that the generalized Einstein equations (with zero energy–stress tensor) are equivalent to those of the Kaluza–Klein theory satisfying a “modified cylinder condition” and having a noncompact extra dimension. This opens a possibility to consider Kaluza–Klein models with a noncompact extra dimension that remains invisible for a macroscopic observer. In our approach, this extra dimension is not an additional physical space–time dimension but appears because of the generalization of the derivation concept.
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5

Ni, Wei-Tou. "Genesis of general relativity — A concise exposition." International Journal of Modern Physics D 25, no. 14 (December 2016): 1630004. http://dx.doi.org/10.1142/s0218271816300044.

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This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier’s discovery of the Mercury perihelion advance anomaly, Michelson–Morley experiment, Eötvös experiment, Newcomb’s improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity (CGR): gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in four-dimentional spacetime and derived the four-dimensional electromagnetic stress–energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended Minkowski’s method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; Abraham, Einstein, and Nordström proposed their versions of scalar theories of gravity in 1911–13; Einstein and Grossmann first used metric as the basic gravitational entity and proposed a “tensor” theory of gravity (the “Entwurf” theory, 1913); Einstein proposed a theory of gravity with Ricci tensor proportional to stress–energy tensor (1915); Einstein, based on 1913 Besso–Einstein collaboration, correctly derived the relativistic perihelion advance formula of his new theory which agreed with observation (1915); Hilbert discovered the Lagrangian for electromagnetic stress–energy tensor and the Lagrangian for the gravitational field (1915), and stated the Hilbert variational principle; Einstein equation of GR was proposed (1915); Einstein published his foundation paper (1916). Subsequent developments and applications in the next two years included Schwarzschild solution (1916), gravitational waves and the quadrupole formula of gravitational radiation (1916, 1918), cosmology and the proposal of cosmological constant (1917), de Sitter solution (1917), Lense–Thirring effect (1918).
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6

DUPRÉ, MAURICE J., and FRANK J. TIPLER. "GENERAL RELATIVITY AS AN ÆTHER THEORY." International Journal of Modern Physics D 21, no. 02 (February 2012): 1250011. http://dx.doi.org/10.1142/s0218271812500113.

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Most early twentieth century relativists — Lorentz, Einstein, Eddington, for examples — claimed that general relativity was merely a theory of the æther. We shall confirm this claim by deriving the Einstein equations using æther theory. We shall use a combination of Lorentz's and Kelvin's conception of the æther. Our derivation of the Einstein equations will not use the vanishing of the covariant divergence of the stress–energy tensor, but instead equate the Ricci tensor to the sum of the usual stress–energy tensor and a stress–energy tensor for the æther, a tensor based on Kelvin's æther theory. A crucial first step is generalizing the Cartan formalism of Newtonian gravity to allow spatial curvature, as conjectured by Gauss and Riemann. In essence, we shall show that the Einstein equations are a special case of Newtonian gravity coupled to a particular type of luminiferous æther. Our derivation of general relativity is simple, and it emphasizes how inevitable general relativity is, given the truth of Newtonian gravity and the Maxwell equations.
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7

Eisinger, Josef. "Thoughts on Einstein and general relativity." Physics Today 69, no. 10 (October 2016): 12. http://dx.doi.org/10.1063/pt.3.3312.

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8

Klainerman, Sergiu. "General Relativity and the Einstein Equations." Classical and Quantum Gravity 27, no. 1 (December 16, 2009): 019001. http://dx.doi.org/10.1088/0264-9381/27/1/019001.

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9

von Borzeszkowski, H. H., and H. J. Treder. "Mach-Einstein doctrine and general relativity." Foundations of Physics 26, no. 7 (July 1996): 929–42. http://dx.doi.org/10.1007/bf02148835.

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10

Kox, A. J. "Einstein, Lorentz, Leiden and general relativity." Classical and Quantum Gravity 10, S (December 1, 1993): S187—S191. http://dx.doi.org/10.1088/0264-9381/10/s/020.

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11

Brügmann, Bernd. "Fundamentals of numerical relativity for gravitational wave sources." Science 361, no. 6400 (July 26, 2018): 366–71. http://dx.doi.org/10.1126/science.aat3363.

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Einstein’s theory of general relativity affords an enormously successful description of gravity. The theory encodes the gravitational interaction in the metric, a tensor field on spacetime that satisfies partial differential equations known as the Einstein equations. This review introduces some of the fundamental concepts of numerical relativity—solving the Einstein equations on the computer—in simple terms. As a primary example, we consider the solution of the general relativistic two-body problem, which features prominently in the new field of gravitational wave astronomy.
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12

Adamo, Tim. "General relativity as a two-dimensional CFT." International Journal of Modern Physics D 24, no. 12 (October 2015): 1544024. http://dx.doi.org/10.1142/s0218271815440241.

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The tree-level scattering amplitudes of general relativity (GR) encode the full nonlinearity of the Einstein field equations. Yet remarkably compact expressions for these amplitudes have been found which seem unrelated to a perturbative expansion of the Einstein–Hilbert action. This suggests an entirely different description of GR which makes this on-shell simplicity manifest. Taking our cue from the tree-level amplitudes, we discuss how such a description can be found. The result is a formulation of GR in terms of a solvable two-dimensional conformal field theory (CFT), with the Einstein equations emerging as quantum consistency conditions.
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13

Daywitt, William C. "General Relativity in the Planck Vacuum Theory." European Journal of Applied Physics 4, no. 4 (August 17, 2022): 45. http://dx.doi.org/10.24018/ejphysics.2022.4.4.180.

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This short paper compares the classical Newton gravitational equation to the Einstein curvature tensor and shows that the two are intimately related. The calculation expands the Newton force to be more in line with the Einstein and Schwarzschild tensors.
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14

FRASCA, MARCO. "STRONG COUPLING EXPANSION FOR GENERAL RELATIVITY." International Journal of Modern Physics D 15, no. 09 (September 2006): 1373–86. http://dx.doi.org/10.1142/s0218271806009091.

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Strong coupling expansion is computed for the Einstein equations in vacuum in the Arnowitt–Deser–Misner (ADM) formalism. The series is given by the duality principle in perturbation theory as presented in M. Frasca, Phys. Rev. A58, 3439 (1998). An example of application is also given for a two-dimensional model of gravity expressed through the Liouville equation showing that the expansion is not trivial and consistent with the exact solution, in agreement with the general analysis. Application to the Einstein equations in vacuum in the ADM formalism shows that the space–time near singularities is driven by space homogeneous equations.
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15

Hess, Peter O. "Pseudo-Complex General Relativity." International Journal of Modern Physics: Conference Series 45 (January 2017): 1760002. http://dx.doi.org/10.1142/s2010194517600023.

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The present status of the pseudo-complex General Relativity is presented. The pcGR includes many known theories with a minimal length. Restricting to its simplest form, an energy-momentum tensor is added at the right hand side of the Einstein equations, representing a dark energy, related to vacuum fluctuations. We use a phenomenological ansatz for the density and discuss observable consequences: Quaisperiodic Oscillations (QPO), effects on accretion disks and gravitational waves.
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16

Will, Clifford M. "The confrontation between general relativity and experiment." Proceedings of the International Astronomical Union 5, S261 (April 2009): 198–99. http://dx.doi.org/10.1017/s174392130999038x.

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AbstractWe review the experimental evidence for Einstein's general relativity. A variety of high precision null experiments confirm the Einstein Equivalence Principle, which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relativity. Binary pulsars test gravitational-wave damping and aspects of strong-field general relativity. During the coming decades, tests of general relativity in new regimes may be possible. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests via precise measurements of the properties of gravitational waves. Future efforts using X-ray, infrared, gamma-ray and gravitational-wave astronomy may one day test general relativity in the strong-field regime near black holes and neutron stars.
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17

Canepa, G., A. S. Cattaneo, and M. Schiavina. "General Relativity and the AKSZ Construction." Communications in Mathematical Physics 385, no. 3 (July 2, 2021): 1571–614. http://dx.doi.org/10.1007/s00220-021-04127-6.

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AbstractIn this note the AKSZ construction is applied to the BFV description of the reduced phase space of the Einstein–Hilbert and of the Palatini–Cartan theories in every space-time dimension greater than two. In the former case one obtains a BV theory for the first-order formulation of Einstein–Hilbert theory, in the latter a BV theory for Palatini–Cartan theory with a partial implementation of the torsion-free condition already on the space of fields. All theories described here are BV versions of the same classical system on cylinders. The AKSZ implementations we present have the advantage of yielding a compatible BV–BFV description, which is the required starting point for a quantization in presence of a boundary.
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18

BLOHMANN, CHRISTIAN, MARCO CEZAR BARBOSA FERNANDES, and ALAN WEINSTEIN. "GROUPOID SYMMETRY AND CONSTRAINTS IN GENERAL RELATIVITY." Communications in Contemporary Mathematics 15, no. 01 (January 22, 2013): 1250061. http://dx.doi.org/10.1142/s0219199712500617.

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When the vacuum Einstein equations are cast in the form of Hamiltonian evolution equations, the initial data lie in the cotangent bundle of the manifold [Formula: see text] of Riemannian metrics on a Cauchy hypersurface Σ. As in every Lagrangian field theory with symmetries, the initial data must satisfy constraints. But, unlike those of gauge theories, the constraints of general relativity do not arise as momenta of any Hamiltonian group action. In this paper, we show that the bracket relations among the constraints of general relativity are identical to the bracket relations in the Lie algebroid of a groupoid consisting of diffeomorphisms between space-like hypersurfaces in spacetimes. A direct connection is still missing between the constraints themselves, whose definition is closely related to the Einstein equations, and our groupoid, in which the Einstein equations play no role at all. We discuss some of the difficulties involved in making such a connection. In an appendix, we develop some aspects of diffeology, the basic framework for our treatment of function spaces.
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19

Howard, D., J. Stachel, and Wolfgang Drechsler. "Einstein and the History of General Relativity." Physics Today 44, no. 2 (February 1991): 96–98. http://dx.doi.org/10.1063/1.2809998.

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20

Anderson, Arlen, Yvonne Choquet-Bruchat, and James W. York Jr. "Einstein-Bianchi hyperbolic system for general relativity." Topological Methods in Nonlinear Analysis 10, no. 2 (December 1, 1997): 353. http://dx.doi.org/10.12775/tmna.1997.037.

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21

Will, Clifford M. "Einstein and the History of General Relativity." American Journal of Physics 58, no. 9 (September 1990): 894. http://dx.doi.org/10.1119/1.16345.

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22

Katore, S. D., R. S. Rane, K. S. Wankhade, and N. K. Sarkate. "Einstein-Rosen inflationary Universe in general relativity." Pramana 74, no. 4 (April 2010): 669–73. http://dx.doi.org/10.1007/s12043-010-0059-y.

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23

SHARIF, M., and TASNIM FATIMA. "ENERGY–MOMENTUM DISTRIBUTION: A CRUCIAL PROBLEM IN GENERAL RELATIVITY." International Journal of Modern Physics A 20, no. 18 (July 20, 2005): 4309–30. http://dx.doi.org/10.1142/s0217751x05020793.

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This paper is aimed to elaborate the problem of energy–momentum in general relativity. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for two exact solutions of Einstein field equations. The space–times under consideration are the nonnull Einstein–Maxwell solutions and the singularity-free cosmological model. The electromagnetic generalization of the Gödel solution and the Gödel metric become special cases of the nonnull Einstein–Maxwell solutions. It turns out that these prescriptions do not provide consistent results for any of these space–times. These inconsistent results verify the well-known proposal that the idea of localization does not follow the lines of pseudotensorial construction but instead follows from the energy–momentum tensor itself. These differences can also be understood with the help of the Hamiltonian approach.
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24

Will, Clifford M. "General Relativity confronts experiment." Symposium - International Astronomical Union 114 (1986): 355–67. http://dx.doi.org/10.1017/s0074180900148387.

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We review the status of experimental tests of general relativity. These include tests of the Einstein Equivalence Principle, which requires that gravitation be described by a curved-spacetime, “metric” theory of gravity. General relativity is consistent with all tests to date, including the “classical tests”: light deflection using radio interferometers, radar time delay using Viking Mars landers, and the perihelion shift of Mercury; and tests of the strong equivalence principle, such as lunar laser ranging tests of the “Nordtvedt effect”, and tests for variations in G. We also review ten years of observations of the Binary Pulsar, in which the first evidence for gravitational radiation has been found.
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25

Gomez, Alfonso Leon Guillen. "Einstein's gravitation is Einstein-Grossmann's equations." JOURNAL OF ADVANCES IN PHYSICS 11, no. 3 (December 28, 2015): 3099–110. http://dx.doi.org/10.24297/jap.v11i3.464.

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While the philosophers of science discuss the General Relativity, the mathematical physicists do not question it. Therefore, there is a conflict. From the theoretical point view “the question of precisely what Einstein discovered remains unanswered, for we have no consensus over the exact nature of the theory's foundations. Is this the theory that extends the relativity of motion from inertial motion to accelerated motion, as Einstein contended? Or is it just a theory that treats gravitation geometrically in the spacetime setting?”. “The voices of dissent proclaim that Einstein was mistaken over the fundamental ideas of his own theory and that their basic principles are simply incompatible with this theory. Many newer texts make no mention of the principles Einstein listed as fundamental to his theory; they appear as neither axiom nor theorem. At best, they are recalled as ideas of purely historical importance in the theory's formation. The very name General Relativity is now routinely condemned as a misnomer and its use often zealously avoided in favour of, say, Einstein's theory of gravitation What has complicated an easy resolution of the debate are the alterations of Einstein's own position on the foundations of his theory”, (Norton, 1993) [1]. Of other hand from the mathematical point view the “General Relativity had been formulated as a messy set of partial differential equations in a single coordinate system. People were so pleased when they found a solution that they didn't care that it probably had no physical significance” (Hawking and Penrose, 1996) [2]. So, during a time, the declaration of quantum theorists: “I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation.” (Hawking and Penrose, 1996) [2] seemed to solve the problem, but recently achieved with the help of the tightly and collectively synchronized clocks in orbit frontally contradicts fundamental assumptions of the theory of Relativity. These observations are in disagree from predictions of the theory of Relativity. (Hatch, 2004a, 2004b, 2007) [3,4,5]. The mathematical model was developed first by Grossmann who presented it, in 1913, as the mathematical part of the Entwurf theory, still referred to a curved Minkowski spacetime. Einstein completed the mathematical model, in 1915, formulated for Riemann´s spacetimes. In this paper, we present as of General Relativity currently remains only the mathematical model, darkened with the results of Hatch and, course, we conclude that a Einstein´s gravity theory does not exist.
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26

Yakovlev, D. G. "General relativity and neutron stars." International Journal of Modern Physics A 31, no. 02n03 (January 20, 2016): 1641017. http://dx.doi.org/10.1142/s0217751x16410177.

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General Relativity affects all major aspects of neutron star structure and evolution including radiation from the surface, neutron star models, evolution in compact binaries. It is widely used for neutron star mass measurements and for studying properties of superdense matter in neutron stars. Observations of neutron stars help testing General Relativity and planning gravitational wave experiments. No deviations from Einstein Theory of Gravity have been detected so far from observations of neutron stars.
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27

Al Hosni, Kareema, and Mudhahir Al Ajmi. "Comparison between Three Paradigms of General Relativity." Physical Sciences Forum 2, no. 1 (February 22, 2021): 48. http://dx.doi.org/10.3390/ecu2021-09280.

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Gravity formulated as a classical gauge theory is based on the Mach principle in terms of curvature scalar R by A. Einstein. The original idea of Einstein limits the gravity to act as a curvature in spacetime. However, there exist other possible classical fields such as torsion and non-metricity. The aim of this paper is to make a compatible comparison between three paradigms: Gravity as curvature via Einstein–Hilbert action, Teleparallel Gravity (TEGR) and Coincidence Gravity (CGR). In TEGR, a flat spacetime is considered as well as an asymmetric connection metric. In CGR, gravity is constructed in an equally flat, tortionless spacetime, which is ascribed to non-metricity. The strength and weakness of each formulation is tested in the framework of a homogeneous and isotropic cosmological background. Mainly, the equivalence between GR and TEGR is examined at the level of equation of motion. Furthermore, we study the interactions between dark energy, dark matter and radiation, and the stability of these models is explored. The implications of the interaction were tested in both early and late epochs of the universe. It has been found that mostly there is a similarity of description of the evolution of the universe provided by GR and TEGR, while CGR always showed different description.
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28

GOLUBEV, M. B., and S. R. KELNER. "POINT CHARGE SELF-ENERGY IN THE GENERAL RELATIVITY." International Journal of Modern Physics A 20, no. 11 (April 30, 2005): 2288–93. http://dx.doi.org/10.1142/s0217751x05024511.

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Singularities in the metric of the classical solutions to the Einstein equations (Schwarzschild, Kerr, Reissner – Nordström and Kerr – Newman solutions) lead to appearance of generalized functions in the Einstein tensor that are not usually taken into consideration. The generalized functions can be of a more complex nature than the Dirac δ-function. To study them, a technique has been used based on a limiting solution sequence. The solutions are shown to satisfy the Einstein equations everywhere, if the energy-momentum tensor has a relevant singular addition of non-electromagnetic origin. When the addition is included, the total energy proves finite and equal to mc2, while for the Kerr and Kerr–Newman solutions the angular momentum is mca. As the Reissner–Nordström and Kerr–Newman solutions correspond to the point charge in the classical electrodynamics, the result obtained allows us to view the point charge self-energy divergence problem in a new fashion.
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Cremaschini, Claudio, and Massimo Tessarotto. "Manifest Covariant Hamiltonian Theory of General Relativity." Applied Physics Research 8, no. 2 (March 16, 2016): 60. http://dx.doi.org/10.5539/apr.v8n2p60.

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The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called “DeDonder-Weyl” formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.
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30

YEOM, Dong-han. "The Beginning of General Relativity." Physics and High Technology 30, no. 6 (June 30, 2021): 30–35. http://dx.doi.org/10.3938/phit.30.020.

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In this article, we briefly review the motivations behind general relativity. We first discuss the basics of classical physics, including the equations of motion and the field equations. Newtonian mechanics assumes absolute space and time, but this can be philosophically unnatural. Einstein constructed a general theory of classical physics with covariance for the general choice of coordinate systems. This theory is known as general relativity. Finally, we briefly mention how this theory is completed, how this theory is verified, and what can be the future of general relativity.
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31

Bean, Rachel, Pedro G. Ferreira, and Andy Taylor. "A new golden age: testing general relativity with cosmology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1957 (December 28, 2011): 4941–46. http://dx.doi.org/10.1098/rsta.2011.0366.

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Gravity drives the evolution of the Universe and is at the heart of its complexity. Einstein's field equations can be used to work out the detailed dynamics of space and time and to calculate the emergence of large-scale structure in the distribution of galaxies and radiation. Over the past few years, it has become clear that cosmological observations can be used not only to constrain different world models within the context of Einstein gravity but also to constrain the theory of gravity itself. In this article, we look at different aspects of this new field in which cosmology is used to test theories of gravity with a wide range of observations.
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32

Lo, C. Y. "Comments on errors of “A simplified two-body problem in general relativity” by S Hod And Rectification of General Relativity." JOURNAL OF ADVANCES IN PHYSICS 12, no. 1 (July 30, 2016): 4188–96. http://dx.doi.org/10.24297/jap.v12i1.175.

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Hod claimed to have a method to deal with a simplified two-body problem. The basic error of Hod and the previous researchers is that they failed to see that in general relativity there is no bounded dynamic solution for a two-body problem. A common error is that the linearized equation is considered as always providing a valid approximation in mathematics. However, validity of the linearization is proven only for the static and the stable cases when the gravitational wave is not involved. In a dynamic problem when gravitational wave is involved, since it is proven in 1995 that there is no bounded dynamic solution, the process of linearization is not valid in mathematics. This is the difference between Einstein and Gullstrand who suspected that a dynamic solution does not exist. In fact, for the dynamic case, the Einstein equation and the linearized equation are essentially independent equations, and the perturbation approach is not valid. Note that the linearized equation is a linearization of the Lorentz-Levi-Einstein equation, which has bounded dynamic solutions but not the Einstein equation, which has no bounded dynamic solution. Because of inadequacy in non-linear mathematics, many had made errors without knowing them.
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33

Dudek, Marta, and Janusz Garecki. "General Relativity with a Positive Cosmological Constant Λ as a Gauge Theory." Axioms 8, no. 1 (February 21, 2019): 24. http://dx.doi.org/10.3390/axioms8010024.

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In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein–Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein–Palatini (EP) action, and then we present how Einstein fields equations can be derived from it. In the next section, we study Einstein–Palatini action integral for general relativity with a positive cosmological constant Λ in terms of the corrected curvature Ω c o r . We see that in terms of Ω c o r this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω c o r .
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PANTOJA, N. R., and H. RAGO. "DISTRIBUTIONAL SOURCES IN GENERAL RELATIVITY: TWO POINT-LIKE EXAMPLES REVISITED." International Journal of Modern Physics D 11, no. 09 (October 2002): 1479–99. http://dx.doi.org/10.1142/s021827180200213x.

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A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the density [Formula: see text], associated to the Einstein tensor [Formula: see text] of the regularized metric, rather than the Einstein tensor itself, be a distribution and (ii) the regularized metric be a continuous metric with a discontinuous extrinsic curvature across a non-null hypersurface of codimension one. In this paper, the curvature and Einstein tensors of the geometries associated to point sources in the (2 + 1)-dimensional gravity and the Schwarzschild spacetime are considered. In both examples the regularized metrics are continuous regular metrics, as defined by Geroch and Traschen, with well defined distributional curvature tensors at all the intermediate steps of the calculation. The limit in which the support of these curvature tensors tends to the singular region of the original spacetime is studied and the results are contrasted with the ones obtained in previous works.
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35

Ahsan, Zafar, and Musavvir Ali. "Curvature tensor for the spacetime of general relativity." International Journal of Geometric Methods in Modern Physics 14, no. 05 (April 13, 2017): 1750078. http://dx.doi.org/10.1142/s0219887817500785.

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In the differential geometry of certain [Formula: see text]-structures, the role of [Formula: see text]-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing [Formula: see text]-tensor have been considered and the existence of Killing and conformal Killing vector fields has been established. Perfect fluid spacetimes with vanishing [Formula: see text]-tensor have also been considered. The divergence of [Formula: see text]-tensor is studied in detail and it is seen, among other results, that a perfect fluid spacetime with conserved [Formula: see text]-tensor represents either an Einstein space or a Friedmann-Robertson-Walker cosmological model.
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36

Petti, Richard James. "Derivation of Einstein–Cartan theory from general relativity." International Journal of Geometric Methods in Modern Physics 18, no. 06 (April 19, 2021): 2150083. http://dx.doi.org/10.1142/s0219887821500833.

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This paper derives the elements of classical Einstein–Cartan theory (EC) from classical general relativity (GR) in two ways. (I) Derive discrete versions of torsion (translational holonomy) and the spin-torsion field equation of EC from one Kerr solution in GR. (II) Derive the field equations of EC as the continuum limit of a distribution of many Kerr masses in classical GR. The convergence computations employ “epsilon-delta” arguments, and are not as rigorous as convergence in Sobolev norm. Inequality constraints needed for convergence restrict the limits from continuing to an infinitesimal length scale. EC enables modeling exchange of intrinsic and orbital angular momentum, which GR cannot do. Derivation of EC from GR strengthens the case for EC and for new physics derived from EC.
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37

Thuan, Vo Van. "Klein-Gordon-Fock equation from Einstein general relativity." Communications in Physics 26, no. 2 (September 27, 2016): 181. http://dx.doi.org/10.15625/0868-3166/26/2/7866.

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A time-space symmetry based cylindrical model of geometrical dynamics was proposed. Accordingly, the solution of Einstein gravitational equation in vacuum has a duality: an exponential solution and a wave-like one. The former leads to a "microscopic" cosmological model with Hubble expansion. Due to interaction of a Higgs-like cosmological potential, the original time-space symmetry is spontaneously broken, inducing a strong time-like curvature and a weak space-like deviation curve. In the result, the wave-like solution leads to Klein-Gordon-Fock equation which would serve an explicit approach to the problem of consistency between quantum mechanics and general relativity.
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38

Hall, G. S., and D. P. Lonie. "Projective equivalence of Einstein spaces in general relativity." Classical and Quantum Gravity 26, no. 12 (May 27, 2009): 125009. http://dx.doi.org/10.1088/0264-9381/26/12/125009.

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39

Will, C. M. "General Relativity at 75: How Right Was Einstein?" Science 250, no. 4982 (November 9, 1990): 770–76. http://dx.doi.org/10.1126/science.250.4982.770.

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40

Goulart, E. "Mimicking General Relativity with Newtonian Dynamics." ISRN Mathematical Physics 2012 (November 10, 2012): 1–15. http://dx.doi.org/10.5402/2012/260951.

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The aim of this paper is twofolded. (1) Showing that Newtonian mechanics of point particles in static potentials admits an alternative description in terms of effective riemannian spacetimes. (2) Using the above geometrization scheme to investigate aspects of the gravitational field as it appears in the Einstein theory. It is shown that the mechanical (3 + 1) effective metrics are quite similar to Gordon's metric, as it is suggested by the well-known optical-mechanical analogy. Some special potentials are worked out.
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41

Taylor, Emory. "Falsification of Einstein’s relativity." Physics Essays 34, no. 4 (December 24, 2021): 578–81. http://dx.doi.org/10.4006/0836-1398-34.4.578.

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In 1915, Einstein published general relativity. In 1916, he published a German language book about relativity, which contained his marble table thought experiment for explaining a continuum. Without realizing it, Einstein introduced a quantized two-dimensional discontinuum geometry and inadvertently falsified the marble table thought experiment continuum, which falsified relativity. The foundations of physics do not now (and never did) include a fundamentally sound relativistic theory to account for macroscopic phenomena. It is well known the success of relativity and its singularity problem indicate general relativity is a first approximation of a more fundamental theory. Combine that indication with the falsification of relativity and it is apparent, without speculation, that relativity is now and always was a first approximation of a more fundamental theory. A possible way forward to the more fundamental theory is developing a discontinuum physics based on the quantized two-dimensional discontinuum geometry or an algebraic version of it. Such discontinuum physics is not presented, because it is beyond the scope of this paper.
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42

BONA, C., and J. MASSÓ. "NUMERICAL RELATIVITY: EVOLVING SPACETIME." International Journal of Modern Physics C 04, no. 04 (August 1993): 883–907. http://dx.doi.org/10.1142/s0129183193000690.

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The construction of numerical solutions of Einstein's General Relativity equations is formulated as an initial-value problem. The space-plus-time (3 + 1) decomposition of the spacetime metric tensor is used to discuss the structure of the field equations. The resulting evolution system is shown to depend in a crucial way on the coordinate gauge. The mandatory use of singularity avoiding coordinate conditions (like maximal slicing or similar gauges) is explained. A brief historical review of Numerical Relativity is included, showing the enormous effort in constructing codes based in these gauges, which lead to non-hyperbolic evolution systems, using "ad hoc" numerical techniques. A new family of first order hyperbolic evolution systems for the vacuum Einstein field equations in the harmonic slicing gauge is presented. This family depends on a symmetric 3 × 3 array of parameters which can be used to scale the dynamical variables in future numerical applications.
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43

Lo, C. Y. "Incompleteness of General Relativity, Einstein's Errors, and Related Experiments-- American Physical Society March meeting, Z23 5, 2015 --." JOURNAL OF ADVANCES IN PHYSICS 8, no. 2 (April 15, 2015): 2135–47. http://dx.doi.org/10.24297/jap.v8i2.1515.

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General relativity is incomplete since it does not include the gravitational radiation reaction force and the interaction of gravitation with charged particles. General relativity is confusing because Einstein's covariance principle is invalid in physics. Moreover, there is no bounded dynamic solution for the Einstein equation. Thus, Gullstrand is right and the 1993 Nobel Prize for Physics press release is incorrect. Moreover, awards to Christodoulou reflect the blind faith toward Einstein and accumulated errors in mathematics. Note that the Einstein equation with an electromagnetic wave source has no valid solution unless a photonic energy-stress tensor with an anti-gravitational coupling is added. Thus, the photonic energy includes gravitational energy. The existence of anti-gravity coupling implies that the energy conditions in space-time singularity theorems of Hawking and Penrose cannot be satisfied, and thus are irrelevant. Also, the positive mass theorem of Yau and Schoen is misleading, though considered as an achievement by the Fields Medal. E = mc2 is invalid for the electromagnetic energy alone. The discovery of the charge-mass interaction establishes the need for unification of electromagnetism and gravitation and would explain many puzzles. Experimental investigations for further results are important.
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44

DADHICH, NARESH. "ON GRAVITO-ELECTROMAGNETIC DUALITY IN GENERAL RELATIVITY." Modern Physics Letters A 14, no. 12 (April 20, 1999): 759–63. http://dx.doi.org/10.1142/s0217732399000808.

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In analogy with the electromagnetic theory, we resolve the Riemann curvature into electric and magnetic parts and consider the analogous duality transformation which keeps the Einstein action for vacuum invariant. It is remarkable that the duality symmetry of the action also leads to the vacuum field equation without cosmological constant. Further invariance of the vacuum equation and the action under the gravito-electric duality require gravitational constant to change sign.
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Ramirez, Marcos A., and Daniel Aparicio. "Evolution of thin shells in D-dimensional general relativity." International Journal of Modern Physics D 28, no. 04 (March 2019): 1950069. http://dx.doi.org/10.1142/s021827181950069x.

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In this paper, we consider singular timelike spherical hypersurfaces embedded in a [Formula: see text]-dimensional spherically symmetric bulk spacetime which is an electrovacuum solution of Einstein equations with cosmological constant. We analyze the different possibilities regarding the orientation of the gradient of the standard [Formula: see text] coordinate in relation to the shell. Then we study the dynamics according to Einstein equations for arbitrary matter satisfying the dominant energy condition. In particular, we thoroughly analyze the asymptotic dynamics for both the small and large-shell-radius limits. We also study the main qualitative aspects of the dynamics of shells made of linear barotropic fluids that satisfy the dominant energy condition. Finally, we prove weak cosmic censorship for this class of solutions.
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MOTT, GERALD. "A REVIEW OF EINSTEIN'S THEORY OF SPECIAL RELATIVITY." International Journal of Modern Physics E 15, no. 03 (April 2006): 755–60. http://dx.doi.org/10.1142/s0218301306004594.

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Using only the descriptions and the results of the 'thought experiment' contained in Einstein's seminal 1905 paper, proofs are offered which show that the transformation equations of Einstein's special relativity apply only to the joint use in his experiment of point sources of light and point reflectors. Further, it is shown that two different special relativities could have been invented by Einstein and, because they possess differing space and time contraction factors, they cannot co-exist and, therefore, both must be discarded.
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47

S, Kalimuthu. "On the shape and fate of our Universe." Annals of Mathematics and Physics 5, no. 1 (March 25, 2022): 011–12. http://dx.doi.org/10.17352/amp.000034.

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Einstein’s special and general theories of relativity revolutionized physics and cosmology. Newton assumed four identities namely mass, energy, space, and time. He told that space is absolute. Einstein modified and refined Newtonian concepts s by postulating that mass-energy and space-time. This enabled Einstein to find special relativity theory which predicted the variance of mass with velocity, the equivalent of mass and energy, time dilation, and length contraction. The extension and generalization of special relativity theory is the outcome of general relativity theory which is the geometrical interpretation of gravity. Almost all the predictions of Einstein’s general relativity theory have been experimentally verified. By delving into the equations of general relativity, the famous Russian mathematician Alexander Freedman found that the geometry of our Universe has only three possibilities, namely, open, closed, and flat. Freedman’s publication in the 1920s paved the way to study the geometry and fate of our Universe. Recently, NASA’s WMAP spacecraft and ESA’s Planck probes and observations revealed that the geometry of our Universe is flat with a marginal error of 0.04%. But to this day, there is no mathematical proof for these observations. In this short work, by applying the multiplication and division laws of number theory to cosmic triangles the author attempts to show that the shape/geometry of our Universe is FLAT.
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48

Schweber, Silvan S. "Einstein and Oppenheimer: Interactions and Intersections." Science in Context 19, no. 4 (December 2006): 513–59. http://dx.doi.org/10.1017/s0269889706001050.

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ArgumentThe paper is an exploration of the interactions between Einstein and Oppenheimer. It highlights the sharp differences in Einstein's and Oppenheimer's approach to physics, in their presentation of self as iconic figures, and in their relation to the communities they considered themselves part of. To understand their differing approaches to physics it briefly reviews the kinds of unifications that took place in physics during the first two-thirds of the twentieth century and points to the 1961 MIT centennial celebration to demonstrate the potency of Einstein's vision that there might be a fundamental theory from which all known theories could be derived. It also briefly reviews various aspects of the development of theoretical physics and of general relativity in the first two-thirds of the twentieth century, to better understand the context of the sharp, negative remarks that Oppenheimer made about Einstein and about his theory of general relativity in 1965 on the occasion of the tenth anniversary of Einstein's death. To answer the question: “Why the antagonism on Oppenheimer's part?” it looks at Oppenheimer's and Einstein's relation to their Jewish roots, their stance regarding nationalism, and their philosophical commitments.
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Illy, J�zsef. "Einstein teaches Lorentz, Lorentz teaches Einstein their collaboration in general relativity, 1913?1920." Archive for History of Exact Sciences 39, no. 3 (1989): 247–89. http://dx.doi.org/10.1007/bf00329868.

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50

Vishwakarma, Ram. "Einstein and Beyond: A Critical Perspective on General Relativity." Universe 2, no. 2 (May 30, 2016): 11. http://dx.doi.org/10.3390/universe2020011.

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