The Neil Gehrels Swift Observatory followed up 18 gravitational wave (GW) triggers from the LIGO/Virgo collaboration during the O3 observing run in 2019/2020, performing approximately 6500 pointings in total. Of these events, four were finally classified (if real) as binary black hole (BH) triggers, six as binary neutron star (NS) events, two each of NSBH and Mass Gap triggers, one an unmodelled (Burst) trigger, and the remaining three were subsequently retracted. Thus far, four of these O3 triggers have been formally confirmed as real gravitational wave events. While no likely electromagnetic counterparts to any of these GW events have been identified in the X-ray data (to an average upper limit of 3.60 x 10^{-12} erg cm^{-2} s^{-1} over 0.3-10 keV), or at other wavelengths, we present a summary of all the Swift-XRT observations performed during O3, together with typical upper limits for each trigger observed. The majority of X-ray sources detected during O3 were previously uncatalogued; while some of these will be new (transient) sources, others are simply too faint to have been detected by earlier survey missions such as ROSAT. The all-sky survey currently being performed by eROSITA will be a very useful comparison for future observing runs, reducing the number of apparent candidate X-ray counterparts by up to 95 per cent.
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