On the energy content of electromagnetic and gravitational plane waves through super-energy tensors

Abstract

The energy content of (exact) electromagnetic and gravitational plane waves is studied in terms of super-energy tensors (the Bel, Bel-Robinson and the -less familiar-Chevreton tensors) and natural observers. Starting from the case of single waves, the more interesting situation of colliding waves is then discussed, where the nonlinearities of the Einstein's theory play an important role. The causality properties of the super-momentum four vectors associated with each of these tensors are also investigated when passing from the single-wave regions to the interaction region.PACS number: 04.20.Cv

Cylindrical gravitational waves: C-energy, super-energy and associated dynamical effects

“…The latter were introduced for vacuum gravitational fields in order to provide a definition of local energy density (super-energy density) and energy flux (super-Poynting vector) in complete formal analogy with electromagnetism. Their properties have been extensively investigated over the years and applications to many different contexts, including gravitational wave spacetimes, have been discussed [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. A conserved (super-momentum) four vector can be formed also in this case [28,37], carrying the twofold information of the super-energy density and the spatial supermomentum density as measured by a given observer family.…”