Geodesic
Energy-momentum of gravitational waves in the general theory of relativity
Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 2, pp. 167-175

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It is shown that if we follow closely the method of calculating the “flux of energy” of gravitational waves, suggested by Einstein and use only the generally covariant Lagrangian density $\sqrt{-g}R$, then we get the value of the “flux of energy” of gravitational waves equal to zero. Thus the way which was chosen by Einstein and which leads to introducing the noncovariant “pseudotensors” into the covariant physical theory, leads also to the zero value of the “energy” in general relativity theory. 
@article{TMF_1977_32_2_a1,
     author = {A. A. Logunov and V. N. Folomeshkin},
     title = {Energy-momentum of gravitational waves in the general theory of relativity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {167--175},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1977_32_2_a1/}
}
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A. A. Logunov; V. N. Folomeshkin. Energy-momentum of gravitational waves in the general theory of relativity. Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 2, pp. 167-175. http://geodesic.mathdoc.fr/item/TMF_1977_32_2_a1/