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Atiyah-Hitchin in five-dimensional Einstein-Gauss-Bonnet gravity. (English) Zbl 1421.83104

Summary: We construct a new class of stationary exact solutions to five-dimensional Einstein-Gauss-Bonnet gravity. The solutions are based on four-dimensional self-dual Atiyah-Hitchin geometry. We find analytical solutions to the five-dimensional metric function that are regular everywhere. We find some constraints on the possible physical solutions by investigating the solutions numerically. We also study the behavior of the solutions in the extremal limits of the Atiyah-Hitchin geometry. In the extremal limits, the Atiyah-Hitchin metric reduces to a bolt structure and Euclidean Taub-NUT space, respectively. In these limits, the five-dimensional metric function approaches to a constant value and infinity, respectively. We find that the asymptotic metrics are regular everywhere.

MSC:

83E15 Kaluza-Klein and other higher-dimensional theories
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
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