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Journal articles on the topic 'Mathematical relativity'

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Author: Grafiati

Published: 4 June 2021

Last updated: 29 January 2023

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1

Cederbaum, Carla, Mihalis Dafermos, James Isenberg, and Hans Ringström. "Mathematical General Relativity." Oberwolfach Reports 15, no. 3 (August 26, 2019): 2157–251. http://dx.doi.org/10.4171/owr/2018/36.

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2

Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 9, no. 3 (2012): 2269–333. http://dx.doi.org/10.4171/owr/2012/37.

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3

Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 12, no. 3 (2015): 1867–935. http://dx.doi.org/10.4171/owr/2015/33.

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4

Chruściel, Piotr T., Gregory J. Galloway, and Daniel Pollack. "Mathematical general relativity: A sampler." Bulletin of the American Mathematical Society 47, no. 4 (2010): 567. http://dx.doi.org/10.1090/s0273-0979-2010-01304-5.

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5

Cederbaum, Carla, Mihalis Dafermos, James A. Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 18, no. 3 (November 25, 2022): 2157–267. http://dx.doi.org/10.4171/owr/2021/40.

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6

Hall, Graham. "Some remarks on mathematical general relativity theory." Filomat 29, no. 10 (2015): 2403–10. http://dx.doi.org/10.2298/fil1510403h.

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This paper gives a brief survey of the development of general relativity theory starting from Newtonian theory and Euclidean geometry and proceeding through to special relativity and finally to general relativity and relativistic cosmology.

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7

Pommaret, Jean-Francois. "The Mathematical Foundations of General Relativity Revisited." Journal of Modern Physics 04, no. 08 (2013): 223–39. http://dx.doi.org/10.4236/jmp.2013.48a022.

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8

Pereboom, Derk. "Mathematical expressibility, perceptual relativity, and secondary qualities." Studies in History and Philosophy of Science Part A 22, no. 1 (March 1991): 63–88. http://dx.doi.org/10.1016/0039-3681(91)90015-k.

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9

Andersson, Lars. "On the relation between mathematical and numerical relativity." Classical and Quantum Gravity 23, no. 16 (July 27, 2006): S307—S317. http://dx.doi.org/10.1088/0264-9381/23/16/s02.

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10

Gadre, Nitin Ramchandra. "Mathematical model II. Basic particle and special relativity." AIP Advances 1, no. 1 (March 2011): 012106. http://dx.doi.org/10.1063/1.3559461.

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11

Choquet-Bruhat, Yvonne. "Results and Open Problems in Mathematical General Relativity." Milan Journal of Mathematics 75, no. 1 (May 23, 2007): 273–89. http://dx.doi.org/10.1007/s00032-007-0067-7.

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12

McCall, Martin, and Dan Censor. "Relativity and mathematical tools: Waves in moving media." American Journal of Physics 75, no. 12 (December 2007): 1134–40. http://dx.doi.org/10.1119/1.2772281.

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13

Bolstein, Arthur. "The mathematical logic failure of Einstein's special relativity." Kybernetes 32, no. 7/8 (October 2003): 943. http://dx.doi.org/10.1108/03684920310483108.

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14

Seidel, Edward, and Wai-Mo Suen. "NUMERICAL RELATIVITY." International Journal of Modern Physics C 05, no. 02 (April 1994): 181–87. http://dx.doi.org/10.1142/s012918319400012x.

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The present status of numerical relativity is reviewed. There are five closely interconnected aspects of numerical relativity: (1) Formulation. The general covariant Einstein equations are reformulated in a way suitable for numerical study by separating the 4-dimensional spacetime into a 3-dimensional space evolving in time. (2) Techniques. A set of tools is developed for determining gauge choices, setting boundary and initial conditions, handling spacetime singularities, etc. As required by the special physical and mathematical properties of general relativity, such techniques are indispensable for the numerical evolutions of spacetime. (3) Coding. The optimal use of parallel processing is crucial for many problems in numerical relativity, due to the intrinsic complexity of the theory. (4) Visualization. Numerical relativity is about the evolutions of 3-dimensional geometric structures. There are special demands on visualization. (5) Interpretation and Understanding. The integration of numerical data in relativity into a consistent physical picture is complicated by gauge and coordinate degrees of freedoms and other difficulties. We give a brief overview of the progress made in these areas.

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15

Czajko, Jakub. "MATHEMATICAL EXPANSION OF SPECIAL THEORY OF RELATIVITY ONTO ACCELERATIONS." Journal of Fundamental Mathematics and Applications (JFMA) 4, no. 1 (July 1, 2021): 69–89. http://dx.doi.org/10.14710/jfma.v4i1.10197.

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The special theory of relativity (STR) is operationally expanded onto orthogonal accelerations: normal and binormal that complement the instantaneous tangential speed and thus can be structurally extended into operationally complete 4D spacetime without defying the STR. Thus the former classic Lorentz factor, which defines proper time differential can be expanded onto within a trihedron moving in the Frenet frame (T,N,B). Since the tangential speed which was formerly assumed as being always constant, expands onto effective normal and binormal speeds ensuing from the normal and binormal accelerations, the expanded formula conforms to the former Lorentz factor. The obvious though previously overlooked fact that in order to change an initial speed one must apply accelerations (or decelerations, which are reverse accelerations), made the Einstein’s STR incomplete for it did not apply to nongravitational selfpropelled motion. Like a toy car lacking accelerator pedal, the STR could drive nowhere. Yet some scientists were teaching for over 115 years that the incomplete STR is just fine by pretending that gravity should take care of the absent accelerator. But gravity could not drive cars along even surface of earth. Gravity could only pull the car down along with the physics that peddled the nonsense while suppressing attempts at its rectification. The expanded formula neither defies the STR nor the general theory of relativity (GTR) which is just radial theory of gravitation. In fact, the expanded formula complements the STR and thus it supplements the GTR too. The famous Hafele-Keating experiments virtually confirmed the validity of the expanded formula proposed here.

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16

Herbert, R. T. "The Relativity of Simultaneity." Philosophy 62, no. 242 (October 1987): 455–71. http://dx.doi.org/10.1017/s0031819100039036.

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In connection with the special theory of relativity, Einstein made use of a now familiar thought experiment1 involving two lightning flashes, a railway train, and an embankment. Whether he used it merely to help explain the theory to others or whether it played a role in the theory's very generation as well is perhaps a matter of conjecture. However, physicist Richard Feynman, for one, believes that Einstein first conceived his theories in the visualizations of thought experiments and developed their mathematical formulations afterwards. According to a recent magazine essay, ‘Einstein came to an understanding about relativity by imagining people going up in elevators and beaming light back and forth between rocket ships.

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17

Czajko, Jakub. "Mathematical extension of special relativity into three-dimensional internal acceleration." Physics Essays 35, no. 2 (June 27, 2022): 165–70. http://dx.doi.org/10.4006/0836-1398-35.2.165.

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The special theory of relativity (STR) has already been expanded onto normal and binormal subcomponents of an internal acceleration visible within 3D trihedron moving in Frenet frame (T,N,B) along the trajectory curve, in addition to the constant tangential speed of classical STR. Now the STR is extended into tangential, normal, and binormal subcomponents of total internal acceleration in the (moving, curving, and twisting/torsing) trihedron via the varying total internal speed that is extracted from the external speed, which is allowed to vary now with the extended proper/moving time in the external length-based space within operationally imaginary but physically real internal domain of the elapsing proper/moving time. The temporarily emerging extra internal acceleration also implies temporarily arising extra internal forces that could affect airplanes in flight just as they affect the moving zero-dimensional mathematical point. For even an invisible, i.e., mathematically imaginary, force is still physically real active force.

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18

STEINBAUER, R., and M. KUNZINGER. "GENERALISED PSEUDO-RIEMANNIAN GEOMETRY FOR GENERAL RELATIVITY." International Journal of Modern Physics A 17, no. 20 (August 10, 2002): 2776. http://dx.doi.org/10.1142/s0217751x0201203x.

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The study of singular spacetimes by distributional methods faces the fundamental obstacle of the inherent nonlinearity of the field equations. Staying strictly within the distributional (in particular: linear) regime, as determined by Geroch and Traschen2 excludes a number of physically interesting examples (e.g., cosmic strings). In recent years, several authors have therefore employed nonlinear theories of generalized functions (Colombeau algebras, in particular) to tackle general relativistic problems1,5,8. Under the influence of these applications in general relativity the nonlinear theory of generalized functions itself has undergone a rapid development lately, resulting in a diffeomorphism invariant global theory of nonlinear generalized functions on manifolds3,4,6. In particular, a generalized pseudo-Riemannian geometry allowing for a rigorous treatment of generalized (distributional) spacetime metrics has been developed7. It is the purpose of this talk to present these new mathematical methods themselves as well as a number of applications in mathematical relativity.

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19

Minguzzi, E. "Affine Sphere Relativity." Communications in Mathematical Physics 350, no. 2 (November 23, 2016): 749–801. http://dx.doi.org/10.1007/s00220-016-2802-9.

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20

Spears, James W. "Approaching special relativity in complex time." Canadian Journal of Physics 95, no. 10 (October 2017): 923–26. http://dx.doi.org/10.1139/cjp-2017-0089.

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Algebraic techniques are employed to extend time in the complex plane. We then use the framework to examine the fundamental postulates of special relativity. Generalizing the notion of time introduces the reader to a unique perspective on the universality of light speed according to Einstein. In the context of complex time we will describe the mathematical conditions in which light speed universality arises. Using high level terminology we then develop a categorization scheme applicable to physical theories that assume light speed is universal.

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21

Rössler, Otto E., Hans H. Diebner, and Werner Pabst. "Micro Relativity." Zeitschrift für Naturforschung A 52, no. 8-9 (September 1, 1997): 593–99. http://dx.doi.org/10.1515/zna-1997-8-908.

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Abstract A new synthesis based on microscopic classical thinking is attempted in the spirit of the molecular-dynamics-simulation (MDS) paradigm. Leibniz’s idea that joint scale transformations cancel out is invoked. Boltzmann discovered that a time reversal in the whole universe is undetectable from the inside. As a corollary, objective micro time reversals occur in the interface between a subsystem and the rest of the universe, whenever the former undergoes a time reversal. This is shown to occur in a generic class of Hamiltonian systems. The “microinterface” arrived at generalizes the macro frame of relativity to the micro realm. Micro relativity comprises Bohr’s idea of an observer-relative complementarity and Everett’s idea of an observer-relative state. As in relativity proper, a multiplicity of worlds (cuts) exist. For the inhabitants of an artificial MDS universe, therefore a radically new option is available: world change technology.

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22

KLAINERMAN, SERGIU. "RECENT RESULTS IN MATHEMATICAL GR." International Journal of Modern Physics D 22, no. 06 (April 28, 2013): 1330012. http://dx.doi.org/10.1142/s0218271813300127.

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23

Lamberov, Lev D. "THREE ABSENT FACTS OF MATHEMATICAL STRUCTURALISM." Вестник Пермского университета. Философия. Психология. Социология, no. 3 (2022): 389–98. http://dx.doi.org/10.17072/2078-7898/2022-3-389-398.

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The mathematical structuralism of M. Resnik is a possible solution to the problems posed by P. Benacerraf for any adequate philosophy of mathematics. In the paper, the epistemological part of the concept is briefly outlined, and it is shown how, according to M. Resnik, we can obtain the knowledge of mathematical objects by disregarding the perceptual data. The ontological part, according to which con-sistency is taken as a criterion of existence, is also considered. To understand positions, M. Resnik uses the metaphor of a geometrical point. Thus, positions cannot be compared with one another in case they belong to different structures just as points cannot be individuated in case they do not belong to the same plane. Mathematical structures can be in relations of congruence, occurrence, and definitional equiva-lence, but there is no identity relation for them since the positions of the structures do not necessarily co-incide. In addition, the paper compares M. Resnik’s conception of structural relativity with W.V.O. Quine’s ontological relativity. From the conception of structural relativity naturally follows what can be called the doctrine of three types of absent facts. Each type of absent facts is explained separately, then it is demonstrated that some interpretations of P. Benacerraf’s identification problem are incorrect. Keywords: mathematical structuralism, mathematical object, structure, identity, ontological relativity.

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24

Fiscaletti, Davide. "Dynamic Quantum Vacuum and Relativity." Annales Universitatis Mariae Curie-Sklodowska, sectio AAA – Physica 71 (February 23, 2017): 11. http://dx.doi.org/10.17951/aaa.2016.71.11.

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<p>A model of a three-dimensional dynamic quantum vacuum with variable energy density is proposed. In this model, time we measure with clocks is only a mathematical parameter of changes running in quantum vacuum. Mass and gravity are carried by the variable energy density of quantum vacuum. Each elementary particle is a structure of quantum vacuum and diminishes the quantum vacuum energy density. Symmetry “particle – diminished energy density of quantum vacuum” is the fundamental symmetry of the universe which gives origin to the inertial and gravitational mass. Special relativity’s Sagnac effect in GPS system and important predictions of general relativity such as precessions of the planets, the Shapiro time delay of light signals in a gravitational field and the geodetic and frame-dragging effects recently tested by Gravity Probe B, have origin in the dynamics of the quantum vacuum which rotates with the earth.</p>

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25

Eskew, Russell Clark. "Altering the Principle of Relativity." Applied Physics Research 10, no. 3 (May 31, 2018): 21. http://dx.doi.org/10.5539/apr.v10n3p23.

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A unique hyperbolic geometry paradigm requires altering the Relativistic principle that absolute velocity is unmeasurable. There is no absolute velocity, but in the case where a constant velocity is made from a half-angle velocity, a variable velocity is the same as (absolute) acceleration. Relativity is based on local Lorentz geometry. Our mathematical geometry constructs circle and hyperbola vectors with hyperbolic terms in an original formulation of complex numbers. We use a point on a hyperbola as a frame of reference. A theory is given that time and our velocity are inversely related. The physical laws of motion by Galileo, Newton and Einstein are forged using the half-angle velocity to electromagnetic velocity. The field of kinetic, potential and gravitational force accelerations is established. An experiment exemplifies the math from the Earth’s frame of reference. We discover a possible dark energy and gravitational accelerations and a geometry of gravitational collapse.

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26

Eskew, Russell Clark. "Suspending the Principle of Relativity." Applied Physics Research 8, no. 2 (March 29, 2016): 82. http://dx.doi.org/10.5539/apr.v8n2p82.

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A unique hyperbolic geometry paradigm requires suspending the Relativistic principle that absolute velocity is unmeasurable. The idea that of two observers each sees the same constant velocity, therefore there is no absolute velocity, is true only because Relativity uses a particular Lorentz geometry. Our mathematical geometry constructs circle and hyperbola vectors with hyperbolic terms in an original formulation of complex numbers. We use a point on a hyperbola as a frame of reference. A theory of time is given. The physical laws of motion by Galileo, Newton and Einstein are forged using the absolute velocity and the precondition to electromagnetic velocity. The field of real and fictitious force accelerations is established. We utilize Galilean Invariance to measure absolute velocity. An experiment exemplifies the math from the Earth’s frame of reference. But Relativity is based on local Lorentz geometry. We discover a possible dark energy and gravitational accelerations and a geometry of gravitational collapse.

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27

Kolhe, K. G. "Relativity of Pseudo-Spherical Concept and Hartree-Fock Concept for Condensed Matter." International Journal for Research in Applied Science and Engineering Technology 10, no. 8 (August 31, 2022): 1839–41. http://dx.doi.org/10.22214/ijraset.2022.46529.

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Abstract: The function Fn,l (r) ;the radial part of of the pseudo-wave function k (r,  ,  ) is expressed in terms of ion-core electron density, n,l (r) and its relation with the radial part Pn,l (r ) of Hartree- Fock wave function. A new mathematical function psl (x) called as pseudo-spherical function has been developed which is similar to other mathematical functions, and helpful in determining many types of electron densities. The physical and mathematical developments on various aspects such as functional densities have been described. It is further emphasized that Fn,l (r) and Pn,l (r) functions and core electron density at different electronic states of the atom that both the functions posses strong correlationship. Study concludes that the present development resulted into an innovative simpler path in the orientation of condensed matter as well as Mathematical Physics.

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28

Süssmann, Georg. "A Simple Deviation from Relativity." Zeitschrift für Naturforschung A 48, no. 8-9 (September 1, 1993): 932–34. http://dx.doi.org/10.1515/zna-1993-8-916.

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Abstract A test of special relativity is proposed by conceiving a rather natural generalization of the minkowskian spacetime. This is mathematically similar to generalizing the notion of finite dimensional Banach space of the related Hilbert space concept. A corresponding experiment might be feasible with appropriate quantum optical methods.

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29

Fil’chenkov, M. L., and Yu P. Laptev. "MATHEMATICAL MODELS IN THEORETICAL PHYSICS." Metafizika, no. 3 (December 15, 2020): 64–68. http://dx.doi.org/10.22363/2224-7580-2020-3-64-68.

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Quantum theory and relativity theory as well as possible reconciliation have been analyzed from the viewpoint of mathematical models being used in them, experimental affirmation, interpretations and their association with dualistic paradigms.

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30

ROMERO, C., J. B. FONSECA-NETO, and M. L. PUCHEU. "GENERAL RELATIVITY AND WEYL FRAMES." International Journal of Modern Physics A 26, no. 22 (September 10, 2011): 3721–29. http://dx.doi.org/10.1142/s0217751x11054188.

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We present the general theory of relativity in the language of a non-Riemannian geometry, namely, Weyl geometry. We show that the new mathematical formalism may lead to different pictures of the same gravitational phenomena, by making use of the concept of Weyl frames. We show that, in this formalism, it is possible to construct a scalar-tensor gravitational theory that is invariant with respect to the so-called Weyl tranformations and reduces to general relativity in a particular frame, the Riemann frame. In this approach the Weyl geometry plays a fundamental role since it appears as the natural geometrical setting of the theory when viewed in an arbitrary frame. Our starting point is to build an action that is manifestly invariant with respect to Weyl transformations. When this action is expressed in more familiar terms of Riemannian geometry we find that the theory has some similarities with Brans-Dicke theory of gravity. We illustrate this point with an example in which a known Brans-Dicke vacuum solution may appear when reinterpreted in a particular Weyl frame.

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31

ROMERO, C., J. B. FONSECA-NETO, and M. L. PUCHEU. "GENERAL RELATIVITY AND WEYL FRAMES." International Journal of Modern Physics: Conference Series 03 (January 2011): 27–35. http://dx.doi.org/10.1142/s2010194511001115.

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We present the general theory of relativity in the language of a non-Riemannian geometry, namely, Weyl geometry. We show that the new mathematical formalism may lead to different pictures of the same gravitational phenomena, by making use of the concept of Weyl frames. We show that, in this formalism, it is possible to construct a scalar-tensor gravitational theory that is invariant with respect to the so-called Weyl tranformations and reduces to general relativity in a particular frame, the Riemann frame. In this approach the Weyl geometry plays a fundamental role since it appears as the natural geometrical setting of the theory when viewed in an arbitrary frame. Our starting point is to build an action that is manifestly invariant with respect to Weyl transformations. When this action is expressed in more familiar terms of Riemannian geometry we find that the theory has some similarities with Brans-Dicke theory of gravity. We illustrate this point with an example in which a known Brans-Dicke vacuum solution may appear when reinterpreted in a particular Weyl frame.

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32

Schwartz, Charles. "Tachyons in general relativity." Journal of Mathematical Physics 52, no. 5 (May 2011): 052501. http://dx.doi.org/10.1063/1.3587119.

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33

Natário, José. "Book review: “A Mathematical Introduction to General Relativity” by Amol Sasane." European Mathematical Society Magazine, no. 124 (March 2, 2022): 59–60. http://dx.doi.org/10.4171/mag/75.

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34

Kassir, Radwan M. "On Lorentz transformation and special relativity: Critical mathematical analyses and findings." Physics Essays 27, no. 1 (March 5, 2014): 16–25. http://dx.doi.org/10.4006/0836-1398-27.1.16.

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35

Berisha, Valbona, and Shukri Klinaku. "The only pure mathematical error in the special theory of relativity." Physics Essays 30, no. 4 (December 8, 2017): 442–43. http://dx.doi.org/10.4006/0836-1398-30.4.442.

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36

Arunasalam, V. "Intrinsic Theoretical Power and Mathematical Beauty of Relativity, and Ultimate Reality." Physics Essays 16, no. 1 (March 2003): 104–30. http://dx.doi.org/10.4006/1.3025556.

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37

Jaramillo, José Luis, Juan Antonio Valiente Kroon, and Eric Gourgoulhon. "From geometry to numerics: interdisciplinary aspects in mathematical and numerical relativity." Classical and Quantum Gravity 25, no. 9 (April 22, 2008): 093001. http://dx.doi.org/10.1088/0264-9381/25/9/093001.

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38

Nugayev, R. M. "Paul Dirac’s peculiar synthesis of quantum mechanics and special relativity: an intertheoretic context." Philosophy of Science and Technology 26, no. 2 (2021): 96–109. http://dx.doi.org/10.21146/2413-9084-2021-26-2-96-109.

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One of the key episodes of the history of modern physics – Paul Dirac’s 1928 contrivance of the relativistic theory of the electron – in the context of lucid epistemological model of mature theory change is elicited. The peculiar character of Dirac’s synthesis of special relativity and quantum mechanics is revealed by comparison with Einstein’s methodology of the Gen- eral Relativity creation. The structure of Dirac’s scientific research programme and first and foremost the three pivotal principles that put up its heuristics is scrutinized with special emphasis on the “mathematical beauty”. It is contended that it was the general relativity genesis elicited in Eddington’s masterpiece “The Mathematical Theory of Relativity” that constituted Dirac’s synthetic paradigm with its emphasis on mathematical speculation, continual modification and generalization of the basic axioms and with the Clifford algebra and Weyl’s bispinors playing the dual lead of Riemannian geometry and Einstein’s metrical tensor. It is punctuated that in spite of the relentless Dirac’s remarks underestimating the role of philosophy one can trace its indirect influence through Arthur Eddington’s whimsical philosophy of science grounded on Hermann Weyl’s quasi-Husserlian epistemology. The basic stages of realization of Dirac’s research programme are elicited with a special emphasis on the crossbred (dual) objects’ construction.

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39

Das, Abhishek, and B. G. Sidharth. "Noncommutativity and Relativity." Zeitschrift für Naturforschung A 73, no. 9 (September 25, 2018): 775–80. http://dx.doi.org/10.1515/zna-2018-0085.

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AbstractIn this paper, we endeavour to show that from the noncommutative nature of spacetime one can deduce the concept of relativity, in the sense that velocity cannot be infinite as in the case of Galilean relativity.

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40

Marr, John H. "A novel visualization of the geometry of special relativity." International Journal of Modern Physics C 27, no. 05 (May 2016): 1650055. http://dx.doi.org/10.1142/s0129183116500558.

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The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR that may, by complementing the standard works, aid the understanding of SR and its fundamental principles in a more intuitive way. From the axiom that the velocity of light remains constant to any inertial observer, the geodesic is presented as a line of constant angle on the complex plane across a set of diverging reference frames. The resultant curve is a logarithmic spiral, and this view of the geodesic is extended to illustrate the relativistic Doppler effect, time dilation, length contraction, the twin paradox, and relativistic radar distance in an original way, whilst retaining the essential mathematical relationships of SR. Using a computer-generated graphical representation of photon trajectories allows a visual comparison between the relativistic relationships and their classical counterparts, to visualize the consequences of SR as velocities become relativistic. The model may readily be extended to other situations, and may be found useful in presenting a fresh understanding of SR through geometric visualization.

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41

Krasnobokyi, Yurii, Ihor Tkachenko, and Kateryna Ilnitska. "TO THE METHOD OF STUDYING THE BASICS OF SPECIAL THEORY OF RELATIVITY." Collection of Scientific Papers of Uman State Pedagogical University, no. 2 (June 29, 2022): 166–81. http://dx.doi.org/10.31499/2307-4906.2.2022.262956.

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Special Theory of Relativity (STR) is a fundamental physical theory that underlies modern physics andhas enormous worldview potential. At the same time, in the process of teaching (studying) the elementsof STR in school and higher education institutions face a number of problems. These problems areprimarily related to the complex mathematical apparatus that describes it; consideration of imaginarymodel representations that do not really exist in nature; formation of the concept of “event” anddistinguishing under different initial conditions of the concepts of “relative”, “portable” and“absolute” movements, etc. In this regard, it is important to find ways to improve the methodology ofstudying the elements of STR, which is what this article is about.The article offers one of the tested options for studying the main provisions of the special theory ofrelativity in the general course of physics, which is taught in the programs of physical andmathematical specialties of pedagogical universities. The main approaches on which the proposedmethodology is based are the reference to the principle of conformity in the transformation of physicaltheories from their partial cases to more general ones. In this regard, the limits of application ofclassical Galilean-Newton mechanics in the plane of absolutization by this theory of categories of spaceand time, the simultaneity of events in a different frame of reference, the instantaneous transmission ofinteractions between bodies at a distance, etc. are analyzed.The physical meaning of Einstein’s postulates, which underlie the theory of relativity, regarding thespecial status of the speed of light propagation as a natural phenomenon is clarified. On the basis ofthese postulates, the formulas of the Lorentz coordinate and time transformations are deduced. Aconsistent, detailed derivation of the formula for the transition coefficient from the Galilean coordinateand time transformations (for the transition from one inertial frame of reference to another) to theLorentz coordinate and time transformations, which reflects their relativistic content, is given. Theestablishment of these formulas is based on the mathematical apparatus, which corresponds to the levelof school mathematical training of participants in the educational process. Based on the obtainedresults on the formulas of Lorentz transformations, the relativity of the concepts of “duration ofevents”, “time intervals”, “changes in size and shape of bodies”, etc. is demonstrated mathematically,if they are considered in reference systems that are in motion relative to each other. Keywords: classical mechanics; reference system; the principle of relativity; space-time invariant;coordinate and time conversion.

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42

Lin, De-Hone. "The 2+1-Dimensional Special Relativity." Symmetry 14, no. 11 (November 14, 2022): 2403. http://dx.doi.org/10.3390/sym14112403.

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In the new mathematical description of special relativity in terms of the relativistic velocity space, many physical aspects acquire new geometric meanings. Performing conformal deformations upon the 2-dimensional relativistic velocity space for the (2+1)-dimensional special relativity, we find that these conformal deformations correspond to the generalized Lorentz transformations, which are akin to the ordinary Lorentz transformation, but are morphed by a global rescaling of the polar angle and correspondingly characterized by a topological integral index. The generalized Lorentz transformations keep the two fundamental principles of special relativity intact, suggesting that the indexed generalization may be related to the Bondi–Metzner–Sachs (BMS) group of the asymptotic symmetries of the spacetime metric. Furthermore, we investigate the Doppler effect of light, the Planck photon rocket, and the Thomas precession, affirming that they all remain in the same forms of the standard special relativity under the generalized Lorentz transformation. Additionally, we obtain the general formula of the Thomas precession, which gives a clear geometric meaning from the perspective of the gauge field theory in the relativistic velocity space.

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43

Bricmont, J. "Quantum non-locality and relativity." Journal of Statistical Physics 82, no. 3-4 (February 1996): 1213–16. http://dx.doi.org/10.1007/bf02179810.

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44

Rietdijk, Rachel H. "Spinning particles in general relativity." Theoretical and Mathematical Physics 98, no. 3 (March 1994): 317–25. http://dx.doi.org/10.1007/bf01102208.

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45

Hogan, P. A. "Asymptotic symmetries in general relativity." Letters in Mathematical Physics 10, no. 4 (November 1985): 283–88. http://dx.doi.org/10.1007/bf00420568.

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46

Nikitin, Igor. "Mathematical modeling and visualization of topologically non-trivial solutions in general relativity." Journal of Physics: Conference Series 1730, no. 1 (January 1, 2021): 012074. http://dx.doi.org/10.1088/1742-6596/1730/1/012074.

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Hall, Graham S., and Ugo Bruzzo. "Editors’ preface for the topical issue on “Recent developments in mathematical relativity”." Journal of Geometry and Physics 62, no. 3 (March 2012): 567–68. http://dx.doi.org/10.1016/j.geomphys.2011.05.009.

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48

Koyama, Kazuya. "Gravity beyond general relativity." International Journal of Modern Physics D 27, no. 15 (November 2018): 1848001. http://dx.doi.org/10.1142/s0218271818480012.

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We introduce the standard model of cosmology based on general relativity and discuss its successes and problems. We then discuss motivations to consider gravitational theories beyond general relativity and summarize observational and theoretical constraints that these theories need to satisfy. A special focus is laid on screening mechanisms, which hide deviations from general relativity in the Solar System and enable large modifications to general relativity on astrophysical and cosmological scales. Finally, several modified gravity models are introduced, which satisfy the Solar System constrains as well as the constraint on the speed of gravitational waves obtained from almost simultaneous detections of gravitational waves and gamma ray bursts from a neutron star merger (GW170817/GRB 170817A).

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Huguet, E., M. Le Delliou, and M. Fontanini. "Cartan approach to Teleparallel Equivalent to General Relativity: A review." International Journal of Geometric Methods in Modern Physics 18, supp01 (February 24, 2021): 2140004. http://dx.doi.org/10.1142/s0219887821400041.

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In previous works, questioning the mathematical nature of the connection in the translations gauge theory formulation of Teleparallel Equivalent to General Relativity (TEGR) Theory led us to propose a new formulation using a Cartan connection. In this review, we summarize the presentation of that proposal and discuss it from a gauge theoretic perspective.

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Samokhvalov, Serhii. "About the Symmetry of General Relativity." Journal of Geometry and Symmetry in Physics 55 (2020): 75–103. http://dx.doi.org/10.7546/jgsp-55-2020-75-103.

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