# A Generally Covariant Field Equation for Gravitation and Electromagnetism

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- First Online:

DOI: 10.1023/A:1025365826316

- Cite this article as:
- Evans, M.W. Found Phys Lett (2003) 16: 369. doi:10.1023/A:1025365826316

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## Abstract

A generally covariant field equation is developed for gravitation and electromagnetism by considering the metric vector , where where

*q*^{μ}in curvilinear, non-Euclidean spacetime. The field equation is$$R^\mu - {\text{ }}\frac{1}{2}Rq^\mu = kT^\mu ,$$

*T*^{μ}is the canonical energy-momentum four-vector,*k*the Einstein constant,*R*^{μ}the curvature four-vector, and*R*the Riemann scalar curvature. It is shown that this equation can be written as$$T^\mu = \alpha q^\mu ,$$

*α*is a coefficient defined in terms of*R*,*k*, and the scale factors of the curvilinear coordinate system. Gravitation is described through the Einstein field equation, which is recovered by multiplying both sides by*q*^{μ}. Generally covariant electromagnetism is described by multiplying the foregoing on both sides by the wedge*q*^{ν}. Therefore, gravitation is described by symmetric metric*q*^{μ}*q*^{ν}and electromagnetism by the anti-symmetric defined by the wedge product*q*^{μ}*q*^{ν}.generally covariant field equation for gravitation and electromagnetism

*O*(3) electrodynamics**B**^{(3)}field## Copyright information

© Plenum Publishing Corporation 2003