"Proper distance" in GR I am aware of two meanings of the term "proper distance" in GR. The first is when you have points in flat space-time, or space-time that's locally "flat enough", in which case it is defined as it is in SR, as the Lorentz interval between the two points. This usage of the term implies that one is considering short distances, or is working in a flat space-time. The second is a term used by some cosmologists, for instance, Lineweaver, who uses it as a synonym for "comoving distance". See for instance Expanding Confusion.. (I often wonder why they don't stick with the term comoving distance, but that's besides the point.) Are there any other common usages for "proper distance" in GR? On a related note, what would be the correct terminology to refer to a 'distance' that's measured along a space-like geodesic (specifically a geodesic of the 4-d space-time)?