Abelian decomposition for Einstein's theory and gauge theoretic approach to classical solutions of Einstein's equation

Abstract

In this report, we present some implications of Abelian decomposition of Einsteins theory. Two fundamental solutions for A2- and B2-restricted gravity will be discussed. Indeed A2-decomposition is adapted to describe the topological property of spacetime and B2-decomposition is appropriate to handle all solutions of gravitational waves. And we will propose a new method to solve Einsteins equation in a gauge theoretical way. Using this method some well known solutions will be derived.