Relative moduli spaces of periodic monopoles provide novel examples of
Asymptotically Locally Flat hyperkahler 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 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.Comment: 23 pages, latex. v2: an erroneous formula is corrected, and its
derivation is given. v3 (published version): references adde
