The interply among the magnetism and gravitative fields ought to be vitalin physics as a result of the magnetism force and gravity area unit 2 types ofbasic forces in nature. Within the Lagrangian of the equality Einstein-Maxwelltheory, solely the quadratic term of Maxwell tensor is said on to magnetism andgravitative fields, which may even be looked because the interaction betweenMaxwell field and therefore the spacetime metric tensor. However, the interactions between magnetism field and curvature tensor aren’t enclosed during thismagnetism theory. Drummond et al.
1 found that such quite the couplings maywell be appeared naturally in QED with the gauge boson effective action originating from one-loop vacuum polarization on a sinusoidal background spacetime. During this effective theory, all of the coupling constant area unit terriblytiny and their values area unit of the order of the square of the Arthur Comptonwavelength of the lepton ? since the coupling between the magnetism field andcurvature tensor is simply a quantum development during this case. However,the models with arbitrary coupling constant are investigated wide in refs.2-8for a few physical motivation.