In this paper, we developed, in detail, the geometric structure of a certain type of geometry usually used in physical applications. This paper contains building blocks (BB), tensors of different orders, curves admitted by the geometry and a comparison between this geometry and others used in the literature. Second-order symmetric and skew-symmetric tensors, usually used for physical applications in the context of the geometrization philosophy, are given. Also, in the framework of the same philosophy, the admitted curves can be used as equations of motion of test particles for any field theory constructed in this geometry.

Keywords:

AMSC: 53A35, 53B50

References

1. M. Planck , Über das Gesetz der Energieverteilung im Normalspektrum, Ann. Phys. 309 (1901) 553–563. Crossref, Google Scholar
2. A. Einstein , Die Feldgleichungen der Gravitation, Sitz. Preuss. Akad. Wiss. (1915) 844–847. Google Scholar
3. M. I. Wanas and S. A. Ammar , Spacetime structure and electromagnetism, Mod. Phys. Lett. A 25 (2010) 1705–1721. Link, Web of Science, Google Scholar
4. M. I. Wanas and M. M. Kamal , A field theory with curvature and anticurvature, Adv. High Energy Phys. 2014 (2014) 1–15. Crossref, Web of Science, Google Scholar
5. M. I. Wanas, S. N. Osman and R. I. El-Kholy , Unification principle and a geometric field theory, Open Phys. 13 (2015) 247–262. Crossref, Web of Science, Google Scholar
6. M. I. Wanas, S. A. Ammar and S. A. Refaey , Teleparallel gravity with non-vanishing curvature, Can. J. Phys. 96 (2018) 1373–1383. Crossref, Web of Science, Google Scholar
7. M. I. Wanas, M. M. Kamal and Z. Ismail , A pure geometric approach to the Aharonov–Bohm effect, Ind. J. Phys. 95 (2021) 2865–2871. Crossref, Web of Science, Google Scholar
8. M. I. Wanas and M. M. Kamal, A. M. Sherif and S. S. Abelsalam , Results of space experiments and effect of torsion, Int. J. Geom. Methods Mod. Phys. 17(10) (2020) 2050152. Link, Web of Science, Google Scholar
9. F. I. Mikhail , Tetrad vector fields and generalizing the theory of relativity, Ain Shams Sci. Bul. 6 (1962) 87. Google Scholar
10. R. Adler, M. Bazin and M. Schiffer , Introduction to General Relativity, 2nd edn. (McGraw-Hill, New York, 1975). Google Scholar
11. S. M. Carroll, Lecture Notes on General Relativity, Report number: NSF-ITP/97-147, (1997), arXiv:gr-qc/9712019. Google Scholar
12. S. L. Bazanski , Hamilton–Jacobi formalism for geodesics and geodesic deviations, J. Math. Phys. 30 (1989) 1018–1029. Crossref, Web of Science, Google Scholar
13. M. I. Wanas, M. Melek and M. E. Kahil , New path equations in absolute parallelism geometry, Astrophys. Space Sci. 228 (1995) 273–276. Crossref, Web of Science, Google Scholar
14. Y. Aharonov and D. Bohm , Significance of electromagnetic potentials in quantum theory, Phys. Rev. 115 (1959) 485–491. Crossref, Web of Science, Google Scholar
15. Y. Aharonov and D. Bohm , Further considerations on electromagntic potentials in the quantum theory, Phys. Rev. 123 (1961) 1511. Crossref, Web of Science, Google Scholar
16. M. I. Wanas , Motion of spinning particles in gravitational fields, Astrophys. Space Sci. 258 (1997) 237–248. Crossref, Web of Science, Google Scholar
17. W. M. McCrea and F. I. Mikhail , Vector tetrads and the creation of matter, Proc. Roy. Soc. London A 235 (1956) 11. Crossref, Web of Science, Google Scholar
18. Q. Exirifard , Randers geometry as Mond/dark matter, J. Cosmol. Astropart. Phys. 11 (2015) 026. Crossref, Web of Science, Google Scholar
19. G. Randers , On an asymmetrical metric in the four-space of general relativity, Phys. Rev. 39 (1941) 195–199. Crossref, Google Scholar
20. H. Reissner , Über die Eigengravitation des elektrischen Feldes nach der Einsteinschen Theorie, Ann. Phys. 355(9) (1916) 106–120. Crossref, Google Scholar
21. G. Nordström , On the energy of the gravitation field in Einstein’s theory, Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings 20(2) (1918) 1238–1245. Google Scholar