General relativistic mhd source terms in 3+1 form for the gravitational field equations

In this paper, the compilation of the complete set of Maxwell-Einstein-Magneto hydrodynamics equations is done. These equations determine the self consistent evolution of a relativistic, ideal MHD fluid in a dynamical space time. Our aim is to set down a formulation of the equations that is suitable for numerical integration in full 3+1 dimensions. Subsets of these equations have appeared elsewhere but we reconcile several seemingly different and equivalent forms of equations. Lastly we derive the MHD source terms that appear in Einstein equations. Some special features regarding this paper will be discussed at the time of presentation in congress.