  We consider supergravity with a gravitino lightest supersymmetric particle.
The next-to-lightest supersymmetric particle (NLSP) decays to the gravitino
with lifetime naturally in the range 10^4 - 10^8 s. However, cosmological
constraints exclude lifetimes at the upper end of this range and disfavor
neutralinos as NLSPs, leaving charged sleptons with lifetimes below a year as
the natural NLSP candidates. Decays to gravitinos may therefore be observed by
trapping slepton NLSPs in water tanks placed outside Large Hadron Collider
(LHC) and International Linear Collider (ILC) detectors and draining these
tanks periodically to underground reservoirs where slepton decays may be
observed in quiet environments. We consider 0.1, 1, and 10 kton traps and
optimize their shape and placement. We find that the LHC may trap tens to
thousands of sleptons per year. At the ILC, these results may be improved by an
order of magnitude in some cases by tuning the beam energy to produce slow
sleptons. Precision studies of slepton decays are therefore possible and will
provide direct observations of gravitational effects at colliders; percent
level measurements of the gravitino mass and Newton's constant; precise
determinations of the gravitino's contribution to dark matter and supersymmetry
breaking's contribution to dark energy; quantitative tests of supergravity
relations; and laboratory studies of Big Bang nucleosynthesis and cosmic
microwave background phenomena.
