In teleparallel gravity, the energy and momentum of arbitrary-polarization pp-waves are proportional to the expansion tensor of the freely falling frame, and the gravitational energy density is proportional to its determinant.
Papapetrou, Einstein’s theory of gravitation and flat space, Proc
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Gravitational energy in pp-wave spacetimes
In teleparallel gravity, the energy and momentum of arbitrary-polarization pp-waves are proportional to the expansion tensor of the freely falling frame, and the gravitational energy density is proportional to its determinant.