Gravitational energy in pp-wave spacetimes

The description of the gravitation energy is a long standing problem. Although some success has been achieved, there is no satisfactory solution to this problem yet. Probably the most promising approach to this problem is given by teleparallelism. Many consistent and interesting results have been obtained in the context of the so-called Teleparallel Equivalent of General Relativity, including results obtained with spacetimes that are neither static nor asymptotically flat. One example is the analysis of the plus-polarized $pp$-waves that has been made recently [Phys. Rev. D 108, 044043 (2023)]. In this paper, this analysis is extended to arbitrary polarization and some new results that shows the consistency of the teleparallel approach is obtained.