Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

Wanas, M. I.; Youssef, Nabil L.; Hanafy, W. El; Osman, Samah N.

doi:10.1155/2016/1037849

Cited by 12 publications

(8 citation statements)

References 31 publications

(46 reference statements)

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“…Let e a µ (µ = 1, ..., n) be the coordinate components of the a-th vector field e a , where Greek and Latin indices are constrained by the Einstein summation convention 1 . In this natural space one can construct many linear affine connections [7][8][9][10], for each there is a different associated geometry of the same space. However, one can go to two extreme cases:…”

Section: Vielbein Space and Teleparallelismmentioning

confidence: 99%

Lorenz gauge fixing of f(T) teleparallel cosmology

Hanafy

Nashed

2017

Int. J. Mod. Phys. D

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In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or ΛCDM as separate scenarios. We reconstruct the f (T ) gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and standard model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular f (T ) gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.PACS numbers: 98.80.Qc, 04.20.Cv, 98.80.Cq.

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Section: Vielbein Space and Teleparallelismmentioning

confidence: 99%

Lorenz gauge fixing of f(T) teleparallel cosmology

Hanafy

Nashed

2017

Int. J. Mod. Phys. D

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“…Considering the identity (27) as a generalization of Bianchi second identity in the AP-space (or PAP, see theorems 1 and 2 of Ref. [37]), we can assume that it gives, physically, a tensorial form of a type of conservation. Consequently, it gives rise to the field equations 2…”

Section: A Lagrangian Function In Pap-geometrymentioning

confidence: 99%

A pure geometric theory of gravity and a material distribution

2017

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A field theory is constructed in the context of parameterized absolute parallelism geometry. The theory is shown to be a pure gravity one. It is capable of describing the gravitational field and a material distribution in terms of the geometric structure of the geometry used (the parallelization vector fields). Three tools are used to attribute physical properties to the geometric objects admitted by the theory. Poisson and Laplace equations are obtained in the linearized version of the theory. The spherically symmetric solution of the theory, in free space, is found to coincide with the Schwarzschild exterior solution of the general theory of relativity. The theory respects the weak equivalence principle in free space only. Gravity and material distribution are not minimally coupled.

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“…: Minguzzi 2011;Giné 2010;Aksirov 2009;Hacyan 2009;Tresoldi 2009;Gingras 2008;Stachel 2005;Darrigol 2004;Logunov, Mestvirishvili, Petrov 2004;Martínez 2004;Galison, Burnett 2003;Shima 2002;Rowe 2001;Corry 1998;Miller 1992;Earman, Glymour 1978;Giannoni 1970;Goldberg 1970;etc. 35 Many enough papers discuss Einstein's philosophy being more or less implicit; for example: de Waal, ten Hagen 2020; Laudisa 2017; Wanas, Youssef, El Hanafy, Osman 2016;Agassi 2015;Rindler 2009;Galison, Burnett 2003;Aronov, Boi 1996;Wang 1995;Borzeszkowski, Treder 1993;Pakhomov 1986; https://doi.org/10.33774/coe-2023-0rjbp ORCID: https://orcid.org/0000-0002-9684-8174 Content not peer-reviewed by Cambridge University Press. License: CC BY-NC-SA 4.0 However, one can think of Einstein's general relativity as an only partial resurrection of Newton's ontomathematical project since it refers only to the latter two aforementioned contributions of Newton, but not touching the former one being furthermore properly mathematical (at least for scientific "common sense"): namely that of infinitesimal calculus.…”

Section: More Reflections About What Gravitation Ismentioning

confidence: 99%

Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics

Penchev

2023

Preprint

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Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators.

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Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

Cited by 12 publications

References 31 publications

Lorenz gauge fixing of f(T) teleparallel cosmology

Lorenz gauge fixing of f(T) teleparallel cosmology

A pure geometric theory of gravity and a material distribution

Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics

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