  We construct an asymptotic metric on the moduli space of two centred
hyperbolic monopoles by working in the point particle approximation, that is
treating well-separated monopoles as point particles with an electric, magnetic
and scalar charge and re-interpreting the dynamics of the 2-particle system as
geodesic motion with respect to some metric. The corresponding analysis in the
Euclidean case famously yields the negative mass Taub-NUT metric, which
asymptotically approximates the $L^2$ metric on the moduli space of two
Euclidean monopoles, the Atiyah-Hitchin metric. An important difference with
the Euclidean case is that, due to the absence of Galilean symmetry, in the
hyperbolic case it is not possible to factor out the centre of mass motion.
Nevertheless we show that we can consistently restrict to a 3-dimensional
configuration space by considering antipodal configurations. In complete
parallel with the Euclidean case, the metric that we obtain is then the
hyperbolic analogue of negative mass Taub-NUT. We also show how the metric
obtained is related to the asymptotic form of a hyperbolic analogue of the
Atiyah-Hitchin metric constructed by Hitchin.
