Rain, Hail, and Drip frames of the Schwarzschild-de Sitter Geometry

Various families of coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry have been constructed by generalizing the Painleve-Gullstrand coordinates. Such observers have categorized as being in the rain frame, a hail frame, or a drip frame, by Taylor and Wheeler. This framework naturally progresses into a search for counterparts of these coordinate systems for the Schwarzschild-de Sitter (SdS) geometry. Consideration of local measurements made by a fiducial observer suggests that the conserved Killing quantity which best fits the designation of ``energy'' in the SdS geometry differs from the one which is typically denoted as such. This leads to Painleve-Gullstrand-style coordinate systems for the SdS geometry that differ from the naïve extrapolations of the Schwarzschild or de Sitter geometries.