Energy-Momentum Distribution of Six-Dimensional Geometric Model of Gravitational Field

Abstract

Much work has been done in exploring the energy-momentum distribution of different four-dimensional spacetimes using different prescriptions. In this paper, we intend to explore the energy and momentum density of six-dimensional geometric model of the gravitational field. The model was constructed by postulating a six-dimensional spacetime manifold with a structure of spacetime of absolute parallelism. For this purpose, we consider the metric representing the geometric model and use five prescriptions, namely, Einstein, Landau-Lifshitz, Bergmann-Thomson, Papapetrou, and Möller in the framework of General Relativity. The energy and momentum turn out to be well defined and finite. The comparison of the results shows that Einstein and Bergmann-Thomson prescriptions yield same energy-momentum densities but different from the other three prescriptions. It is mentioning here that the energy vanishes in the case of Möller's prescription and the momentum densities become zero in all the cases.

Keywords

• general relativity
• six dimensional geometric model