A nonminimally coupled, conformally extended Einstein-Maxwell theory of pp-waves

Tekin Dereli̇,Yorgo Şeni̇koğlu

doi:10.3906/fiz-2002-18

Abstract

A nonminimal coupling of Weyl curvatures to electromagnetic fields is considered in Brans-Dicke-Maxwell theory. The gravitational field equations are formulated in a Riemannian spacetime where the spacetime torsion is constrained to zero by the method of Lagrange multipliers in the language of exterior differential forms. The significance and ramifications of nonminimal couplings to gravity are examined in a pp-wave spacetime.

Highlights

Einstein’s theory of general relativity is a theory of gravitation determined by the Riemannian geometry of a 4-dimensional spacetime
The coupled field equations of the theory may be obtained by field variational principle from an action
It is well known that the second order principle where the metric variations of the Levi-Civita connections are taken into account; and the first order (Palatini) where independent variations of the action relative to the metric and connection yield, in these cases, the same set of field equations [4].The fact that the connection is Levi-Civita may be imposed by the method of Lagrange multipliers

Summary

Introduction

Einstein’s theory of general relativity is a theory of gravitation determined by the Riemannian geometry of a 4-dimensional spacetime. The coupled field equations of the theory may be obtained by field variational principle from an action. Electromagnetic fields can be coupled minimally to gravitation by incorporating the Maxwell Lagrangian density 4-form into the total action; and taking independent variations of the electromagnetic fields. We consider nonminimal couplings of gravity and electromagnetic fields in the Lagrangian density.

Results

Conclusion