### Abstract

Relative moduli spaces of periodic monopoles provide novel examples of asymptotically locally flat hyper-Kähler manifolds. By considering the interactions between well-separated periodic monopoles, we infer the asymptotic behavior of their metrics. When the monopole moduli space is four dimensional, this construction yields interesting examples of metrics with a self-dual curvature (gravitational instantons). We discuss their topology and complex geometry. An alternative construction of these gravitational instantons using moduli spaces of Hitchin equations is also described.

Original language | English (US) |
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Article number | 084015 |

Pages (from-to) | 840151-8401510 |

Number of pages | 7561360 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 65 |

Issue number | 8 A |

State | Published - Apr 15 2002 |

Externally published | Yes |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

Cherkis, S. A., & Kapustin, A. (2002). Hyper-Kähler metrics from periodic monopoles.

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,*65*(8 A), 840151-8401510. [084015].