Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Extended Theories of Electrodynamics in $f(R)$ Gravity

Francesco Bajardi, Micol Benetti, Salvatore Capozziello, Abedennour Dib

Abstract

Within the general framework of $f(R)$ gravity, we introduce a function of the electromagnetic curvature invariant $f(\mathbb{F})$ that couples minimally to gravitation to ensure a consistent treatment of curvature functions in these theories. We show that one of the solutions leads to field equations that are a generalization of the Klein-Gordon equation while the other leads to a typically non-linear massless solution. Focusing on flat spacetime, our formalism recovers the Plebanski family of models and Bopp-Podolsky electrodynamics as specific limits. These extensions may have phenomenological consequences in extreme environments, such as the early universe or near charged compact objects, where deviations from classical electrodynamics might be probed.

Extended Theories of Electrodynamics in $f(R)$ Gravity

Abstract

Within the general framework of gravity, we introduce a function of the electromagnetic curvature invariant that couples minimally to gravitation to ensure a consistent treatment of curvature functions in these theories. We show that one of the solutions leads to field equations that are a generalization of the Klein-Gordon equation while the other leads to a typically non-linear massless solution. Focusing on flat spacetime, our formalism recovers the Plebanski family of models and Bopp-Podolsky electrodynamics as specific limits. These extensions may have phenomenological consequences in extreme environments, such as the early universe or near charged compact objects, where deviations from classical electrodynamics might be probed.
Paper Structure (8 sections, 54 equations)

This paper contains 8 sections, 54 equations.

Table of Contents

  1. Introduction
  2. Massive Theories of Electromagnetism
  3. Extended Electromagnetism
  4. Field Equations in the Palatini Formalism
  5. The Maxwell Equations
  6. The case $f(\mathbb{F}, \Box \mathbb{F}, R) \equiv f(\mathbb{F})$
  7. The case $f(\mathbb{F}, \Box \mathbb{F}, R) \equiv f(\mathbb{F}) + h(\Box \mathbb{F}) + g(R)$
  8. Discussion and Conclusions