Non-minimally Coupled Gravitational and Electromagnetic Fields: pp-Wave Solutions

TL;DR

This paper develops a Lagrangian framework for a non-minimally extended Einstein-Maxwell theory, deriving coupled field equations and presenting exact plane wave solutions involving complex spin-2 fields.

Contribution

It introduces a novel Lagrangian formulation for a non-minimally coupled Einstein-Maxwell theory with explicit solutions for plane-fronted waves.

Findings

Derived coupled field equations via variational principle.

Presented exact solutions involving partially massless and massive spin-2 fields.

Extended understanding of non-minimal couplings in gravitational-electromagnetic theories.

Abstract

We give the Lagrangian formulation of a generic non-minimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first order variational principle using the method of Lagrange multipliers. We look for solutions describing plane-fronted Einstein-Maxwell waves with parallel rays. We give a family of exact solutions associated with a partially massless spin-2 photon and a partially massive spin-2 graviton.