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On certain space-times having the fourth component of energy-momentum complex identically zero. (English) Zbl 1098.83524

Summary: We have shown that space-time with purely time-dependent metric potentials have their components of total energy and momentum for any finite volume \((T_i^4+t_i^4)\) identically zero. The vanishing of \((T_i^4+t_i^4)\) also admits a plane-wave metric where \(g_{ij}\)’s are functions of space and time variables, which can be interpreted as representing electromagnetic radiation.

MSC:

83C99 General relativity
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