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Electrodynamics and Spacetime Geometry: Foundations

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Abstract

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

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Acknowledgments

F. C. acknowledges financial support of the Fundação para a Ciência e Tecnologia through the PhD grant with reference PD/BD/128017/2016, funded by FCT (Portugal). F. S. N. L. acknowledges financial support of the Fundação para a Ciência e Tecnologia through an Investigador FCT Research contract, with reference IF/00859/2012, funded by FCT/MCTES (Portugal).

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  1. Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016, Lisbon, Portugal

    Francisco Cabral & Francisco S. N. Lobo

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  1. Francisco Cabral
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  2. Francisco S. N. Lobo
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Correspondence to Francisco S. N. Lobo.

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Cabral, F., Lobo, F.S.N. Electrodynamics and Spacetime Geometry: Foundations. Found Phys 47, 208–228 (2017). https://doi.org/10.1007/s10701-016-0051-6

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