Rotation of gravitational-wave polarization by weak gravitational fields

Abstract

I t was first suggested by BALAZS (1) and shown by PLEBANSKI (2) that, when an electromagnetic wave propagates through a region of weak gravitationM fields, its polarization vector may be rotated about the direction of propagation. BALAZS and BEnTOTTI(3) have found the same result for an arbi t rary vector which is parallelly propagated through the weak-field region. Recently, LAWRENCE, LI~ITER and SZA~OSI (4) have also arrived at the same result for the polarization of massless spinor waves. In this note we wish to make a simple extension of this result to the polarization of tensor gravitational waves. The gravitat ional waves and the weak background field will be first-order perturbations, h,v(x) and 7gv(x), respectively, on a flat background metric: