Electric charge screening by non-minimal couplings of electromagnetic fields to gravity

Abstract

A case of non-minimal couplings between gravity and electromagnetic fields is presented. The field equations are worked out in the language of exterior differential forms. A class of exact charge screening solutions is given with a specific discussion on the polarisation and magnetisation of space-time. The consequences of non-minimal couplings to gravity are examined.

A model of non-minimally coupled gravitation and electromagnetism in (1+2) dimensions

“…Here, what we mean by self-duality 1 is that the Faraday 2-form contains a single electric field component and a magnetic field whose magnitudes are equal. We show that similar to the result in [24], our model admits exact constant self-dual solutions on AdS space-time given that the coupling constants of the model are constrained by two algebraic relations.…”

“…In this manuscript we are going to study a generalisation of topologically massive gravity with electrodynamics that contains RF 2 -type non-minimal couplings between electrodynamics and gravity. Similar toy models in four dimensions has been considered in [20][21][22][23][24] where in general a single RF 2 -type interaction is added to the Einstein-Maxwell theory. Although four dimensional Einstein-Maxwell theory, where the electromagnetic field is minimally coupled to gravity, is classically a well-established theory, non-minimal coupling terms between curvature and electrodynamics may be introduced, motivated by perturbative QED on curved backgrounds, in particular coming from vacuum polarization.…”

“…Motivated by these interactions, in [20][21][22][23][24] the authors consider various extensions of Einstein-Maxwell theory with RF 2 -type interaction terms and look for solutions. Particularly authors, consider an R ab ∧ F ab ⋆ F coupling term and show that a class of exact non-trivial pp-wave solutions exist in [20]; add coupling terms of the form Y (R)F ∧ ⋆F and show that static, spherically symmetric solutions exist; look at exact solutions of anisotropic inflation for the same coupling in [23].…”

“…Particularly authors, consider an R ab ∧ F ab ⋆ F coupling term and show that a class of exact non-trivial pp-wave solutions exist in [20]; add coupling terms of the form Y (R)F ∧ ⋆F and show that static, spherically symmetric solutions exist; look at exact solutions of anisotropic inflation for the same coupling in [23]. Finally in [24] authors consider RF ∧ ⋆F and RF ∧ F couplings and show that there exists a charge screening solution (with vanishing total charge) for this model. That is, a spherically symmetric, asymptotically de Sitter solution with a constant electromagnetic field 2-form exists, provided that the coupling constant for the non-minimal coupling term is related to the radius of space-time in a certain way.…”

Non-Minimally Coupled Einstein-Yang-Mills Field Equations and Wu-Yang Monopoles in Bertotti-Robinson Spacetimes

“…Variational field equations will be derived in the coordinate-independent language of exterior differential forms. We refer to our previous papers for the notation and conventions [18,19,20]. We provide in Section:3 a brief discussion of the unique conformally flat, static, spherically symmetric Bertotti-Robinson solution of the source-free Einstein-Maxwell equations.…”