Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 8

Self-dual cosmological Bianchi IX and VIII metrics

Pages: 2841 – 2857

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n8.a10

Authors

A. Miković (Grupo de Física Matemática, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Portugal; and Departamento de Matemática e COPELABS, Universidade Lusófona, Lisboa, Portugal)

N. Manojlović (Grupo de Física Matemática, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Portugal; and Departamento de Matem´atica, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Faro, Portugal)

Abstract

We show that self-dual Bianchi IX and VIII cosmological models are described by the Nahm dynamical system for an appropriate type of matrices. We construct the general solutions in the case of the diagonal reductions of the corresponding Nahm equations and give the explicit expressions for the corresponding self-dual metrics in the Euclidean and in the Minkowski signature cases.

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Published 5 January 2024