Geometry of non-symmetric metrics and its application to theoretical physics

Q: How can I download an article?

To download an article from SID, first log in to the site, search for the article title, and click on the 'Download Article' option.

Q: How can I download an ISI article?

To download an ISI article on SID, enter the keyword or article title in the search bar, view the relevant results, click on the desired article, and select the 'Download Article' option.

Q: How can I access the SID database?

To access the SID database, visit SID.ir, create an account, and log in to access scientific resources.

Q: Is downloading articles from SID free?

Some articles on SID are available for free, while others require payment. Details are specified on the article's page.

Fasihi Ramandi Ghodratallah

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: Mathematical Researches Year:2023 | Volume:9 | Issue:2 Page(s): 146-156

Download Full-Text

Persian Verion

View:

Download:

Cites:

Information Journal Paper

Title

Geometry of non-symmetric metrics and its application to theoretical physics

Author(s)

Fasihi Ramandi Ghodratallah | Issue Writer Certificate

Keywords

Non-symmetric mterics

Hilbert-Enstein functional

space-time

Abstract

Introduction
‎General ‎relativity ‎is ‎model ‎of ‎nature, ‎especially, ‎of ‎gravity.‎‎ ‎Its ‎cent‎ral ‎assumption ‎is‎ that space, time, and gravity are all aspects of a single entity, ‎cal‎led ‎space-‎time, which is modeled by a 4-dimensional Lorentzian manifold. It analyzes ‎space-‎time, electromagnetism, matter, and their mutual ‎infl‎uences. ‎But ‎the ‎effects ‎of ‎matter ‎and ‎electromagnetism ‎are ‎added ‎to ‎the ‎model ‎in a‎ ‎way‎ ‎which ‎is ‎not ‎directly ‎related ‎to ‎geometry ‎of ‎space-time ‎manifold. ‎In ‎fact, ‎in‎fluences ‎of ‎matter ‎and ‎electromagnetism ‎fields ‎are ‎added ‎to ‎theory ‎under ‎notion ‎of ‎stress-energy ‎tensor. ‎Hence, considering non-symmetric metrics extends this geometry and make a good apparatus to describe other physical quantities.

Material and Methods
In this paper, we consider the geometry of a non-symmetric semi-Riemannian metric on a manifold M. A special class of such metrics contains a semi-Riemannian metric and a symplectic structure on M, simultaneously. Similar to the Levi-Civita connections in semi-Riemannain manifold, we define a new connection which is torsion free and compatible with our symplectic structure. With the help of semi-Riemannian metric, we define and compute the Rcci and scalar curvature of this new connection.

Results and Discussion
Using a natural Lagrangian (which is a generalization of Hilbert-Einstein action) and calculus of variations we derive some new field equations. The equations show that the symmetric part of semi-Riemannain metrics is directly related to gravity and the symplectic part is capable of describing quantities related to matter.

Conclusion
In this work, we present a completely geometric theory of gravity. The Riemannian geometry, which is usually used to formulate gravitational theories adds the notion of matter to space time manifold as the way which is not directly related to geometry of the theory. In this framework, we retrieve Einstein’s field equation and we will show that the distribution of matter in space-time is directly related to symplectic part of our geometry

Multimedia

No record.

Cites

No record.

References

No record.

Cite

Related Journal Papers

No record.

Related Seminar Papers

No record.

Related Plans