The hidden symmetries of multi-centre metrics
This paper is chiefly concerned with the 4-dimensional positive definite Taub-NUT metric, which is relevant to problems in monopole physics. It is shown that this metric ``sits at the intersection of three families of Ricci-flat metrics'', which are discussed in some detail. Thereupon, its symmetries and the corresponding constants of motion of the geodesic equation are investigated. In particular, it is shown that there is a sort of ``hidden symmetry'' giving rise to an analogue of the classical Runge-Lenz vector. Finally, the results are applied to the scattering of BPS monopoles and fluctuations around such monopoles. This is a rather detailed account which presents both new and already known results in a homogeneous manner. As a minor correction, this reviewer would like to remark that Theorem 2.1 does not hold near a zero of the Killing vector field. Correspondingly, Theorem 2.3 has to be modified a little bit.
scientific article; zbMATH DE number 4120976