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Some pairs of neutron star models can intuitively be thought of as being`closer' together than others, in the sense that more precise observationsmight be required to distinguish between them than would be necessary for otherpairs. In this paper, borrowing ideas from the study of geometrodynamics, weintroduce a mathematical formalism to define a geometric distance betweenstellar 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 manifolditself admits the structure of a Riemannian manifold (`configurationmanifold'), which comes equipped with a canonical metric. By thinking of astationary star as being a particular $3+1$ metric, the structure of which isdetermined through the Tolman-Oppenheimer-Volkoff relations and theirgeneralisations, points on a suitably restricted configuration manifold can bethought of as representing different stars, and distances between these pointscan be computed. We develop the necessary mathematical machinery to build theconfiguration manifold of neutron star models, and provide some worked examplesto illustrate how this space might be used in future studies of stellarstructure.

A metric on the space of neutron star models in general relativity and modified gravity