Abstract
The field of time-domain astrophysics has entered the era of Multi-messenger
Astronomy (MMA). One key science goal for the next decade (and beyond) will be
to characterize gravitational wave (GW) and neutrino sources using the next
generation of Extremely Large Telescopes (ELTs). These studies will have a
broad impact across astrophysics, informing our knowledge of the production and
enrichment history of the heaviest chemical elements, constrain the dense
matter equation of state, provide independent constraints on cosmology,
increase our understanding of particle acceleration in shocks and jets, and
study the lives of black holes in the universe. Future GW detectors will
greatly improve their sensitivity during the coming decade, as will
near-infrared telescopes capable of independently finding kilonovae from
neutron star mergers. However, the electromagnetic counterparts to
high-frequency (LIGO/Virgo band) GW sources will be distant and faint and thus
demand ELT capabilities for characterization. ELTs will be important and
necessary contributors to an advanced and complete multi-messenger network.