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

  • Friedrich W. Hehl
  • Yuri N. Obukhov
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 562)


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.


Equivalence Principle Constitutive Function Nonlinear Electrodynamic Regular Black Hole Nonminimal Coupling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Friedrich W. Hehl
    • 1
    • 2
  • Yuri N. Obukhov
    • 3
  1. 1.School of Natural SciencesInstitute for Advanced StudyPrincetonUSA
  2. 2.Institute for Theoretical PhysicsUniversity of CologneKölnGermany
  3. 3.Department of Theoretical PhysicsMoscow State UniversityMoscowRussia

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