Electromagnetic resolution of curvature and gravitational instantons

We study the electromagnetic resolution of the Riemann curvature on a space-time manifold nl with metric g into its electric and magnetic parts relative to a unit timelike vector with respect to g. There exists a duality transformation between the active and passive electric parts which leaves invariant a subclass of field equations which correspond to the generalized gravitational instanton equations. We also discuss various geometric formulations of the equations of gravitational instantons and their generalization which includes as a special case the classical vacuum Einstein equations. Same special solutions and their physical significance are also considered.