  The currently accepted model for gamma-ray burst phenomena involves the
violent formation of a rapidly rotating solar mass black hole. Gravitational
waves should be associated with the black-hole formation, and their detection
would permit this model to be tested, the black hole progenitor (e.g.,
coalescing binary or collapsing stellar core) identified, and the origin of the
gamma rays (within the expanding relativistic fireball or at the point of
impact on the interstellar medium) located. Even upper limits on the
gravitational-wave strength associated with gamma-ray bursts could constrain
the gamma-ray burst model. To do any of these requires joint observations of
gamma-ray burst events with gravitational and gamma-ray detectors. Here we
examine how the quality of an upper limit on the gravitational-wave strength
associated with gamma-ray burst observations depends on the relative
orientation of the gamma-ray-burst and gravitational-wave detectors, and apply
our results to the particular case of the Swift Burst-Alert Telescope (BAT) and
the LIGO gravitational-wave detectors. A result of this investigation is a
science-based ``figure of merit'' that can be used, together with other mission
constraints, to optimize the pointing of the Swift telescope for the detection
of gravitational waves associated with gamma-ray bursts.
