A Unified Theory of Non-Linear Electrodynamics and Gravity

Details A Unified Theory of Non-Linear Electrodynamics and Gravity A Unified Theory of Non-Linear Electrodynamics and Gravity

2010-11-16

arxiv.org/abs/1011.3641v1

Phys.Rev.D83:025023,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 page, no figures

Scientific paper

10.1103/PhysRevD.83.025023

We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B-field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a deformation of (complex) general relativity and electromagnetism, and describes just two propagating polarisations of the graviton and two of the photon. When gravity is switched off the theory becomes the usual non-linear electrodynamics with a general structure function. The Einstein-Maxwell theory can be recovered by sending some of the parameters of the defining potential to zero, but for any generic choice of the potential the theory is indistinguishable from Einstein-Maxwell at low energies. A real theory is obtained by imposing suitable reality conditions. We also study the spherically-symmetric solution and show how the usual Reissner-Nordstrom solution is recovered.

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