Nonconservation of the Newman-Penrose Conserved Quantities

Abstract

We have examined the Newman-Penrose quantities for test fields in a Schwarzschild background. We find that, unless a static condition has prevailed in the infinite past, backscattered electromagnetic and gravitational waves make it impossible to define the quantities as limits at future null infinity. An operational definition in terms of observations at finite radii is possible, but yields quantities which are not conserved.