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

TL;DR

This paper investigates the energy and momentum of Bianchi type III universes using various prescriptions in General Relativity, finding that these quantities generally vanish under certain conditions, supporting Tryon's conjecture of a universe with zero net energy.

Contribution

It applies different energy-momentum complexes to Bianchi type III universes and explores the implications for Tryon's conjecture, extending previous work on Bianchi universes.

Findings

Energy and momentum vanish for Bianchi III universe in Møller prescription.

Energy and momentum vanish when metric parameter h is zero in other prescriptions.

Supports the idea that the universe's net energy may be zero, consistent with Tryon's conjecture.

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.