Non-minimal $\ln(R)F^2$ Couplings of Electromagnetic Fields to Gravity: Static, Spherically Symmetric Solutions

TL;DR

This paper explores non-minimal electromagnetic-gravity couplings involving a logarithmic curvature term, deriving solutions and analyzing horizon properties for static, spherically symmetric spacetimes.

Contribution

It introduces a novel non-minimal coupling model with a logarithmic curvature term and derives static, spherically symmetric solutions with horizon analysis.

Findings

Derived field equations from the non-minimal coupling model.

Obtained static, spherically symmetric solutions that are asymptotically flat.

Analyzed horizon structures depending on model parameters.

Abstract

We investigate the non-minimal couplings between the electromagnetic fields and gravity through the natural logarithm of the curvature scalar. After we give the Lagrangian formulation of the non-minimally coupled theory, we derive field equations by a first order variational principle using the method of Lagrange multipliers. We look at static, spherically symmetric solutions that are asymptotically flat. We discuss the nature of horizons for some candidate black hole solutions according to various values of the parameters $R_0 $ and $a_1$.