On gravito-electromagnetic duality in general relativity

In analogy with the electromagnetic theory, we resolve the Riemann curvatur e into electric and magnetic parts and consider the analogous duality trans formation which keeps the Einstein action for vacuum invariant. It is remar kable that the duality symmetry of the action also leads to the vacuum fiel d equation without cosmological constant. Further invariance of the vacuum equation and the action under the gravito-electric duality require gravitat ional constant to change sign.