Relativistic Maxwell Theory and Einstein Field Equation derived from Variational Principle

In this article, I'll be reviewing relativistic mechanisms using the calculus of variation in the classical limit. The variational principle is considered to be one of the most important mechanisms to build a theory. Newton's second law of motion is a consequence of Euler-Lagrange equations which gives the least (or stationary) trajectory of a particle between any two arbitrary points. I'll the use action principle by deriving the relativistic Maxwell's field equation, geodesic equation, and Einstein's field equation.

Content

Author and article information

Journal

Title: ScienceOpen Preprints

Publisher: ScienceOpen

Publication date (Electronic preprint): 11 November 2021

Affiliations

[1 ] Independent researcher

Author notes

[* ]Email: shubhamsingh2496@ 123456gmail.com .

Author information

Shubham Singh https://orcid.org/0000-0003-3754-7280

Article

DOI: 10.14293/S2199-1006.1.SOR-.PPDWFUG.v1

SO-VID: 405ab2b2-f10e-4b47-b2a8-95cc4cd2b553

License:

This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

History

Date received : 11 November 2021

Data availability: All data generated or analysed during this study are included in this published article (and its supplementary information files).

ScienceOpen disciplines: Mathematical physics,General physics,Theoretical physics

Keywords: Hilbert Action,Einstein's field equation,Varitional Principle,Maxwell's field equation,Special relativity