Some exact non-vacuum Bianchi VI0 and VII0 instantons

TL;DR

This paper presents new exact instanton solutions in general relativity with matter, specifically in Bianchi types VI0 and VII0, including axisymmetric solutions with electromagnetic fields, expanding the understanding of non-vacuum cosmological models.

Contribution

It introduces novel exact instanton solutions in Bianchi VI0 and VII0 classes with stiff fluid and electromagnetic fields, including axisymmetric cases, and compares their behavior to self-dual solutions.

Findings

Solutions are Kähler and belong to specific Bianchi classes.

Qualitative behavior of solutions is analyzed and compared.

Includes axisymmetric solutions with electromagnetic fields.

Abstract

We report some new exact instantons in general relativity. These solutions are K\"ahler and fall into the symmetry classes of Bianchi types VI0 and VII0, with matter content of a stiff fluid. The qualitative behaviour of the solutions is presented, and we compare it to the known results of the corresponding self-dual Bianchi solutions. We also give axisymmetric Bianchi VII0 solutions with an electromagnetic field.