Neutron star mergers, referring to both binary neutron star and neutron star black hole mergers, are the canonical multimessenger events. They have been detected across the electromagnetic spectrum, have recently been detected in gravitational waves, and are likely to produce neutrinos over several decades in energy. The non-thermal prompt and afterglow emission of short gamma-ray bursts and the quasi-thermal emission from the radioactively powered kilonovae provide distinct insights into the physics of neutron star mergers. When combined with direct information on coalescence from gravitational waves and neutrinos these sources may become the best understood astrophysical transients. Multimessenger observations of these cataclysmic events will determine sources of gravitational waves and astrophysical neutrinos, enable precision cosmology, and unique tests of fundamental physics, the origin of heavy elements, the behavior of relativistic jets, and the equation of state of supranuclear matter. In this white paper we present a summary of the science discoveries possible with multimessenger observations of neutron star mergers and provide recommendations to enable them in the new era of time-domain, multimessenger astronomy.
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