  Painlev\'e-Gullstrand coordinates, a very useful tool in spherical horizon
thermodynamics, fail in anti-de Sitter space and in the inner region of
Reissner-Nordstr\"om. We predict this breakdown to occur in any region
containing negative Misner-Sharp-Hernandez quasilocal mass because of repulsive
gravity stopping the motion of PG observers in radial free fall with zero
initial velocity. PG coordinates break down also in the static Einstein
universe for completely different reasons. The more general Martel-Poisson
family of charts, which normally has PG coordinates as a limit, is reported for
static cosmologies (de Sitter, anti-de Sitter and the static Einstein
universe).
