Null Electromagnetic Fields in General Relativity Theory

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Abstract
The existence of null electromagnetic fields, within the frame of the general relativity theory, has been subject to some doubt. We here construct and investigate two solutions of the Maxwell-Einstein equations, representing null electromagnetic fields, and corresponding to unidirectional radiation flow. One of these fields is coupled with transverse plane gravitational waves, and the other one with longitudinal (not necessarily plane) gravitational waves. It is shown that not only the two electromagnetic invariants, but also the fourteen invariants of the Riemann tensor vanish. During the course of this investigation, use is made of Pirani's tetrad formalism in order to simplify Witten's spinor approach to the problem of invariants.