Bivectors in Newman-Penrose formalism in General Relativity -- from electromagnetism to Weyl curvature tensor

Abstract

The use of the bivectors in the General Relativity with Newman-Penrose formalism is important to the description of the exact solutions of the Einstein's field equations. This review is devoted to introduce the basic ideas with calculation details of the bivectors in Newman-Penrose formalism through conversion of the complex self-dual electromagnetic field from orthornormal Minkowski basis to bivectors in the complex null tetrad basis. Furthermore, in this context, it is obtained the complex coefficients of the Weyl tensor in Newman-Penrose formalism.