MG11 
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Numerical evolution for electro-magnetic field around black-hole

There are well known and well established methods to solve numerically electromagnetic wave equations in flat spacetime in electrical engineering field. We will apply this well established methods to solve Einstein-Maxwell equations in general coordinate systems. In this series of works, we want to develope a robust numerical method solving electromagnetic wave propagation in strong gravitational field, that is, in curved spacetime. In this paper, we will concentrate how one can evolve electro-magnetic field in full numerical fashion. We will dvelope finite difference scheme for both electro-magnetic field and gravitational fields.