A Unified Theory of Non-Linear Electrodynamics and Gravity

TL;DR

This paper introduces a unified BF-type theory combining electromagnetism and gravity, which deforms general relativity and reproduces known solutions like Reissner-Nordstrom, offering a new framework for understanding their relationship.

Contribution

It presents a novel BF-type unified theory of electromagnetism and gravity that generalizes Einstein-Maxwell theory and includes known solutions as special cases.

Findings

The theory describes two polarizations of graviton and photon.

It reduces to Einstein-Maxwell at low energies for specific parameters.

Reissner-Nordstrom solution is recovered within this framework.

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.