  Some pairs of neutron star models can intuitively be thought of as being
`closer' together than others, in the sense that more precise observations
might be required to distinguish between them than would be necessary for other
pairs. In this paper, borrowing ideas from the study of geometrodynamics, we
introduce a mathematical formalism to define a geometric distance between
stellar models, to provide a quantitative meaning to this notion of closeness.
In particular, it is known that the set of all metrics on a Riemannian manifold
itself admits the structure of a Riemannian manifold (`configuration
manifold'), which comes equipped with a canonical metric. By thinking of a
stationary star as being a particular $3+1$ metric, the structure of which is
determined through the Tolman-Oppenheimer-Volkoff relations and their
generalisations, points on a suitably restricted configuration manifold can be
thought of as representing different stars, and distances between these points
can be computed. We develop the necessary mathematical machinery to build the
configuration manifold of neutron star models, and provide some worked examples
to illustrate how this space might be used in future studies of stellar
structure.
