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Gyros, Clocks, Interferometers...: Testing Relativistic Graviy in Space pp 479–504Cite as

How Does the Electromagnetic Field Couple to Gravity, in Particular to Metric, Nonmetricity, Torsion, and Curvature?

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Abstract

The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in the laboratory or by observing outer space. (ii) One desires to test out alternatives to Einstein’s gravitational theory, in particular those of a gauge-theoretical nature, like Einstein-Cartan theory or metric-afine gravity.— A clean discussion requires a reflection on the foundations of electrodynamics. If one bases electrodynamics on the conservation laws of electric charge and magnetic flux, one finds Maxwell’s equations expressed in terms of the excitation H = (D,H) and the field strength F = (E,B) without any intervention of the metric or the linear connection of spacetime. In other words, there is still no coupling to gravity. Only the constitutive law H = functional(F) mediates such a coupling. We discuss the different ways of how metric, nonmetricity, torsion, and curvature can come into play here. Along the way, we touch on non-local laws (Mashhoon), non-linear ones (Born-Infeld, Heisenberg-Euler, Plebaśki), linear ones, including the Abelian axion (Ni), and fid a method for deriving the metric from linear electrodynamics (Toupin, Schönberg). Finally, we discuss possible non-minimal coupling schemes.

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Authors and Affiliations

  1. School of Natural Sciences, Institute for Advanced Study, 08540, Princeton, NJ, USA

    Friedrich W. Hehl

  2. Institute for Theoretical Physics, University of Cologne, 50923, Köln, Germany

    Friedrich W. Hehl

  3. Department of Theoretical Physics, Moscow State University, 117234, Moscow, Russia

    Yuri N. Obukhov

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  1. Friedrich W. Hehl
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Editors and Affiliations

  1. Institute for Experimental Physics, Heinrich-Heine-University Düsseldorf, 40225, Düsseldorf, German

    Claus Lämmerzahl

  2. W.W.Hansen Experimental Physics Laboratory, Stanford University, 94305, Stanford, CA, USA

    C. W. Francis Everitt

  3. Institute for Theoretical Physics, University of Cologne, 50923, Köln, Germany

    Friedrich W. Hehl

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Hehl, F.W., Obukhov, Y.N. (2001). How Does the Electromagnetic Field Couple to Gravity, in Particular to Metric, Nonmetricity, Torsion, and Curvature?. In: Lämmerzahl, C., Everitt, C.W.F., Hehl, F.W. (eds) Gyros, Clocks, Interferometers...: Testing Relativistic Graviy in Space. Lecture Notes in Physics, vol 562. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40988-2_25

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