Non-minimal ln (R)F 2 couplings of electromagnetic fields to gravity: static, spherically symmetric solutions

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 .

Gravity and electromagnetism with Y(R)F2-type coupling and magnetic monopole solutions

“…The analysis of the solutions such as horizons and asymptotic behaviors can be found in [35,36]. The metric function (23) with β = −3 give us a Rindler acceleration term which is also obtained from a Dilaton-gravity model in [39,40] to explain some anomalies such as the rotation curves of spiral galaxies and Pioneer anomaly [41,42].…”

“…In this paper, to recover the previous metric functions obtained in [35,36] we deal with certain non-minimal functions Y (R) that involve a new non-minimal coupling constant λ which can be related to cosmological constant.…”

“…Consequently, we find solutions recovering the metric functions in [35,36] in the presence of magnetic field. Thus, we point out that the solutions are asymptotically flat for some values of the parameters in the model and they can provide possible geometries which may explain the flatness of the observed rotational curves of galaxies.…”

“…for some values of the involved parameters (see for example [35]). Nevertheless, naked singularities, evaluated at some future space-time points, could be revealed by an observer, giving observational consequences [47][48][49][50].…”

Regular black hole solutions of the non-minimally coupled Y(R) F2 gravity

“…We obtain gravitational and electromagnetic field equations of the theory by taking infinitesimal variations of the action according to independent variations of {e a }, {ω a b } and {A} [21,22] …”