Here are schematics of some rolled-up x-cτ plots for paths through the (open) center of spherical objects of various mass, from no mass (upper left) to black hole (lower right), inspired by Lewis Carroll Epstein's sketchesEpstein, Lewis Carroll (1895/1994). "Relativity Visualized", (Insight Press, San Fransisco), ch. 9-12 12-4 through 12-7. Free-float trajectories are straight-lines on the "locally-flat" x-cτ surface. Simple gravitational potential models were used to generate the radial profiles, over an axial distance of ±5 radii. The rate of passage of proper-time τ (represented by angular position around the tube azimuth) for an observer at fixed "far-radius" r from the gravitational object's center (represented by distance from the center of each image-panel along the tube's axis), per unit far-time t (represented by distance in any direction on the curved surface), decreases as the tube-diameter increases near a gravitational object's center. Even further, the gravitational Lorentz-factor dt/dτ goes to infinity at the black-hole's event horizon in the bottom right panel so that events happening quickly to a plunging traveler seem to take forever to a far-time observer.