The Momentum 4-Vector Imparted by Gravitational Waves in Bianchi-Type Metrics

Considering the Møller, Weinberg and Qadir-Sharif's definitions in general relativity, we find the momentum 4-vector of the closed universe based on the Bianchi-type metrics. The momentum 4-vector (due to matter plus fields) is found to be zero. This result supports the viewpoints of Albrow and Tryon and extends the previous works by Cooperstock–Israelit, Rosen, Johri et al., Banerjee–Sen and Vargas who investigated the problem of the energy in Friedmann–Robertson–Walker universe and Salt?-Havare who studied the problem of the energy-momentum of the viscous Kasner-type space-times.