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arXiv · 2403.04117

New quasi-Einstein metrics on a two-sphere

Alex Colling·Maciej Dunajski·Hari Kunduri·James Lucietti
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Abstract

We construct all axi-symmetric non-gradient $m$-quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon corresponding to $m=2$, as well as a family of new regular metrics with $m\neq 2$ given in terms of hypergeometric functions. We also show that in the case $m=-1$ with vanishing cosmological constant the only orientable compact solution in dimension two is the flat torus, which proves that there are no compact surfaces with a metrisable affine connection with skew Ricci tensor.

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Alex Colling, Maciej Dunajski, Hari Kunduri, James Lucietti. 2024-03-07. New quasi-Einstein metrics on a two-sphere. https://doi.org/10.1007/s12220-026-02459-0

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