A Perturbative Quantized Twist Embedded in Minkowski Spacetime.

We present results on spatially-structured gravitational waves within the paraxial approximation. Drawing upon analogies between electrodynamics and general relativity, gauge invariant paraxial ``electric'' and ``magnetic'' parts of the Weyl conformal tensor are derived. In this approximation, a new gauge, which we call the paraxial-traceless gauge, is found. The polarization and degrees of freedom are investigated and compared with the Eardley-Newman-Penrose classification. Paraxial gravitational waves are found to share similarities with their electromagnetic counterparts in that they can possess a quantized amount of orbital angular momentum that can be transferred to matter.