A Unified Theory of Non-Linear Electrodynamics and Gravity

Abstract

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.

31 page, no figures

References in corpus (15)

• Making Sense of Non-Hermitian Hamiltonians
• The Plebanski action extended to a unification of gravity and Yang-Mills theory
• Effective metric Lagrangians from an underlying theory with two propagating degrees of freedom
• Renormalizable Non-Metric Quantum Gravity?
• Bi-metric theory of gravity from the non-chiral Plebanski action
• Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations
• Plebanski gravity without the simplicity constraints
• Non-Metric Gravity II: Spherically Symmetric Solution, Missing Mass and Redshifts of Quasars
• Unification of gravity, gauge fields, and Higgs bosons
• Ashtekar's Variables for Arbitrary Gauge Group
• Gravity-Yang-Mills-Higgs unification by enlarging the gauge group
• Towards a unification of gravity and Yang-Mills theory
• Gravity and Yang-Mills Theory: Two Faces of the Same Theory?
• Spherically symmetric black holes in minimally modified self-dual gravity
• Cosmological perturbations in a family of deformations of general relativity

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• Remarks on a nonlinear electromagnetic extension in AdS Reissner-Nordström spacetime
• Foundations of Classical Electrodynamics, Equivalence Principle and Cosmic Interactions: A Short Exposition and an Update
• Analysis of a nonlinear electromagnetic generalization of the Reissner-Nordström black hole
• Spin connection formulations of real Lorentzian General Relativity
• A simple way of unifying the formulas for the Coulomb's law and Newton's law of the universal gravitation: An approach based on membranes