Tryon's conjecture and Energy and momentum of Bianchi Type Universes

Abstract

The energy and momentum of the Bianchi type $III$ universes are obtained using different prescriptions for the energy-momentum complexes in the framework of General Relativity. The energy and momentum of the Bianchi $III$ universe is found to be zero for the M\o{}ller prescription. For all other prescriptions the energy and momentum vanish when the metric parameter $h$ vanishes. In an earlier work, Tripathy et al. \cite{SKT15} have obtained the energy and momentum of Bianchi $VI_h$ metric and found that the energy of the Universe vanish only for $h=-1$. This result raised a question: why this specific choice?. We explored the Tryon's conjecture that 'the Universe must have a zero net value for all conserved quantities' to get some ideas on the specific values of this parameter for Bianchi type Universes.