Cracking the Taub-NUT
Pierre-Philippe Dechant, Anthony N. Lasenby, Michael P. Hobson

TL;DR
This paper explores the relationship between the DLH anisotropic universe model and the Taub-NUT solution, revealing coordinate transformations that clarify their connection and resolve known pathologies in Taub-NUT.
Contribution
It provides explicit mappings between DLH and Taub-NUT models, showing how coordinate choices affect the interpretation of their regions and singularities.
Findings
DLH and Taub-NUT metrics are related by a coordinate transformation.
Vacuum DLH solutions are periodic and map to non-periodic Taub-NUT solutions.
Many Taub-NUT pathologies are due to multivalued coordinate transformations.
Abstract
We present further analysis of an anisotropic, non-singular early universe model that leads to the viable cosmology presented in Dechant et al (arXiv:0809.4335). Although this model (the DLH model) contains scalar field matter, it is reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasi-regular singularity that one can identify with the big-bang. We show that the DLH and Taub-NUT metrics are related by a coordinate transformation, in which the DLH time coordinate plays the role of conformal time for Taub-NUT. Since both models continue through the big-bang, the coordinate transformation can become multivalued. In particular, in mapping from DLH to Taub-NUT, the Taub-NUT time can take only positive values. We present explicit maps between the DLH and Taub-NUT models, with and without a…
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