Here approximate Lie symmetries are used to investigate the problem of energy in general relativity and in particular in gravitational waves (GW). For this purpose second-order approximate symmetries of the system of geodesic equations for the Reissner-Nordstrom, Kerr, Kerr-Newman and GW spacetimes are studied. It is shown that in the second-order approximation, energy must be rescaled for these spacetimes. Since GW spacetimes are time-varying vacuum solutions of Einstein's equations, there is no unambiguous means to define their energy content. Here a definition, using slightly broken symmetries is proposed. A problem is noted with the use of the proposal for pp waves. To attain a better understanding of the implications of this proposal we also use an artificially constructed time-varying non-vacuum plane symmetric metric and evaluate its Weyl and stress-energy tensors so as to obtain the gravitational and matter components separately and compare them with the energy content... Это и многое другое вы найдете в книге Definition of Energy in General Relativity via Approximate Symmetries (Ibrar Hussain)