JNR monopoles

Abstract

We review the theory of JNR, mass $\frac{1}{2}$ hyperbolic monopoles in particular their spectral curves and rational maps. These are used to establish conditions for a spectral curve to be the spectral curve of a JNR monopole and to show that the rational map of a JNR monopole arises by scattering using results of Atiyah. We show that for JNR monopoles the holomorphic sphere has a remarkably simple form and show that this can be used to give a formula for the energy density at infinity. In conclusion, we illustrate some examples of the energy density at infinity of JNR monopoles.