An exact solution for a force-free field electrodynamics accretion disk surrounding a perturbed charged black hole

Abstract: Recently the first real image of the supermassive black hole at the heart of the galaxy M87 successfully has been captured. To explain the behavior of both the observed powerful jets and the electromagnetic accretion disk the Blandford Znajek mechanism, by the Event Horizon Telescope collaboration, has been considered. To justify these phenomena we are seeking an exact solution for a perturbed Rissner-Nordstrom black hole surrounded by a force-free field electrodynamics accretion disk. Although a charged black hole is a toy model, by tending the charge to zero one can obtain the results for a perturbed, rotating, Schwarzschild one immediately. Finding an exact solution in regards to the force-free field electrodynamics as a source for perturbations in different classes of the black holes is may one of the open problems yet. Here to find the solution, different Maxwell's scalars besides the energy-momentum tensor in both tangent and bend backgrounds are calculated. In doing so, the well known Newman-Penrose formalism is considered.