Open AccessMaxwell’s equations from spacetime geometry and the role of Weyl curvature
Author(s) -
Jussi Lindgren,
Jukka Liukkonen
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1956/1/012017
Subject(s) - maxwell's equations in curved spacetime , spacetime , physics , maxwell's equations , curvature , mathematical physics , stationary spacetime , electromagnetic field , covariant transformation , linearized gravity , inhomogeneous electromagnetic wave equation , classical mechanics , general relativity , mathematics of general relativity , quantum field theory in curved spacetime , mathematics , numerical relativity , quantum mechanics , geometry , optical field , quantum gravity , quantum
This research article demonstrates how the field equations of electrodynamics can be shown to be a special case of Einstein field equations of General Relativity. By establishing a special conjecture between the electromagnetic four-potential and the metric of the spacetime, it is first shown how the relativistic wave equation of electrodynamics is a condition for the metric to be Ricci-flat. Moreover, the four-current is identified with a certain four-gradient, which allows one to conjecture that electric charge is related to the covariant divergence of the electromagnetic four-potential. These considerations allow one to understand the Einstein field equations as a nonlinear generalization of Maxwell’s equations. Finally, it is argued that the four-current induces Weyl curvature on the spacetime.