2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217754We write out the explicit form of the metric for a linearized gravitational wave in the transverse-traceless gauge for any multipole, thus generalizing the well-known quadrupole solution of Teukolsky. The solution is derived using the generalized Regge-Wheeler-Zerilli formalism developed by Sarbach and Tiglio.9 pages. Minor corrections, updated references. Final version to appear in Class. Quantum GravGeneral Relativity and Quantum Cosmologytext