  The Advanced X-ray Imaging Satellite (AXIS) promises revolutionary science in
the X-ray and multi-messenger time domain. AXIS will leverage excellent spatial
resolution (<1.5 arcsec), sensitivity (80x that of Swift), and a large
collecting area (5-10x that of Chandra) across a 24-arcmin diameter field of
view to discover and characterize a wide range of X-ray transients from
supernova-shock breakouts to tidal disruption events to highly variable
supermassive black holes. The observatory's ability to localize and monitor
faint X-ray sources opens up new opportunities to hunt for counterparts to
distant binary neutron star mergers, fast radio bursts, and exotic phenomena
like fast X-ray transients. AXIS will offer a response time of <2 hours to
community alerts, enabling studies of gravitational wave sources, high-energy
neutrino emitters, X-ray binaries, magnetars, and other targets of opportunity.
This white paper highlights some of the discovery science that will be driven
by AXIS in this burgeoning field of time domain and multi-messenger
astrophysics.
