With the epochal first detection of gravitational waves from a binary neutron star (NS) merger with the GW170817 event, and its direct confirmation that NS-NS mergers are significant sources of the of the r-process nucleosynthesis of heavy elements, an immense new arena for prompt EM (X-rays through IR and radio) studies of fundamental physics has been opened. Over the next decade, GW observatories will expand in scale and sensitivity so the need for facilities that can provide prompt, high sensitivity, broad-band EM followup becomes more urgent. NS-NS or NS-black hole (BH) mergers will be instantly recognized (and announced) by the LIGO-international collaboration. LSST will be a prime resource for rapid tiling of what will usually be large (~10-100 degree squared) error boxes. X-ray through IR Telescopes in space with (nearly) full-sky access that can rapidly image and tile are crucial for providing the earliest imaging and spectroscopic studies of the kilonova emission immediately following NS-NS mergers. The Time-domain Spectroscopic Observatory (TSO) is a proposed Probe-class 1.3 m telescope at L2, with imaging and spectroscopy (R = 200, 1800) in 4 bands (0.3 - 5 micron) and rapid slew capability to 90% of sky. TSO nUV-mid-IR spectra will enable new constraints on NS structure and nucleosynthesis.
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