Peering into the multi-messenger maelstrom with rapid observations of neutron star mergers

Pairs of neutron stars (NSs) are destined to slowly spiral into each other and eventually merge. By combining extreme gravity, copious emission of gravitational waves, and luminous electromagnetic radiation, these mergers serve as excellent astrophysical laboratories to explore a wide range of fundamental problems: from the formation of relativistic jets to the cosmic production of r-process elements, from the equation of state of cold ultra-dense matter to the expansion rate of the universe. I will discuss how prompt high-energy (X-ray and UV) observations of NS mergers would open a unique window into their central remnant and powerful outflows, and provide us with a new probe of the extreme physics governing compact objects.