On the energy of gravitational waves in the Einstein gravitation theory

It is shown by the examples of exact wave solutions of the Einstein equations that the standard formulation of the energy-momentum problem using the pseudotensors gives the value of energy of gravitational wave equal to zero or sign-changing. It is shown that if the transition to the limit of weak field in the Einstein gravitation theory is performed rigorously, the theory gives the unambigously vanishing result for weak gravitational waves. The well-known non-vanishing result is due to the non-correct transition to the weak field approximation in the Einstein gravitation theory