The scalar wave equation in a Schwarzschild space-time

Abstract

This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild space-time in a neighbourhood of spatial infinity which includes parts of future and past null infinity. The behaviour of such fields is essentially different from that which occurs in a flat space-time. In particular fields which have a Bondi-type expansion in powers of ' r -1 ’ near past null infinity do not have such an expansion near future null infinity. Further solutions which have physically reasonable Cauchy data probably fail to have Bondi-type expansions near null infinity.