A Recursion Operator for Solutions of Einstein Field Equations

Abstract

The (1,1)-tensor field on symplectic manifold that satisfies some integrability conditions is called a recursion operator. It is known the recursion operator is a characterization for integrable systems, and gives constants of motion for integrable systems. We construct recursion operators for the geodesic flows of some solutions of Einstein equation like Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman metrics.