The symmetry of the energy momentum tensor does not necessarily reflect the space-time symmetry: a viscous axially symmetric cosmological solution

TL;DR

This paper explores how the symmetry of the energy-momentum tensor does not necessarily imply the same symmetry in spacetime, presenting new solutions for axially symmetric and spherically symmetric configurations in Einstein's equations.

Contribution

It introduces novel solutions demonstrating that energy-momentum tensor symmetry does not always mirror spacetime symmetry, especially in viscous cosmological contexts.

Findings

Existence of axially symmetric solutions tending to FLRW at infinity

Discovery of spherically symmetric Einstein tensor from axially symmetric spacetime

Identification of solutions with mismatched spacetime and energy tensor symmetries

Abstract

Applying the method of conformal metric to a given static axially symmetric vacuum solution of the Einstein equations, we have shown that there is no solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting the cosmic fluid to be imperfect there are axially symmetric solutions tending to FLRW at space infinity. The solution we have found represents an axially symmetric spacetime leading to a spherically symmetric Einstein tensor. Therefore, we have found a solution of Einstein equations representing a spherically symmetric matter distribution corresponding to a spacetime which does not reflect the same symmetry. We have also found another solution of Einstein equation corresponding to the same energy tensor with spherical symmetry.