The Fermi Large Area Telescope (LAT) has an instantaneous field of view covering $sim 1/5$ of the sky and completes a survey of the full sky every ~3 hours. It provides a continuous, all-sky survey of high-energy gamma-rays, enabling searches for transient phenomena over timescales from milliseconds to years. Among these phenomena could be electromagnetic counterparts to gravitational wave sources. In this paper, we present a detailed study of the LAT observations relevant to Laser Interferometer Gravitational-wave Observatory (LIGO) event GW150904 (Abbott et al. 2016), which is the first direct detection of gravitational waves and has been interpreted as due to coalescence of two stellar-mass black holes. The localization region for GW150904 was outside the LAT field of view at the time of the gravitational wave signal. However, as part of routine survey observations, the LAT observed the entire LIGO localization region within ~70 minutes of the trigger, and thus enabled a comprehensive search for a gamma-ray counterpart to GW150904. The study of the LAT data presented here did not find any potential counterparts to GW150904, but it did provide limits on the presence of a transient counterpart above 100 MeV on timescales of hours to days over the entire GW150904 localization region.
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