Linearization of Einstein's field equations

Abstract

From the Einstein field equations, in a weak-field approximation and for speeds small compared to the speed of light in vacuum, the following system is obtained 

where  is the gravitoelectric field,  is the gravitomagnetic field,  is the space-time-mass current density and    is the spacetime-mass density. This last gravitoelectromagnetic field system is similar to the Maxwell equations, thus showing an analogy between the electromagnetic theory and gravitation.