This award supports research in relativity and relativistic astrophysics and it addresses the priority areas of NSF's "Windows on the Universe" Big Idea. Much excitement has accompanied the beginning of the gravitational wave era ushered in by LIGO's first detections, and this project seeks to study and model the types of systems observed in these detections. In particular, this work will implement a number of physical processes including magnetic and neutrino cooling and heating effects in a numerical code used to simulate such systems. For a few different reasons, a phase transition at very high densities is expected in neutron star matter, and this project will study what range of effects such a transition could have on both the gravitational wave signature and electromagnetic emissions. This study will contribute to furthering the science obtained with LIGO and electromagnetic telescopes as well as future observatories. The project will train students and other personnel and its research will be broadly disseminated.<br/><br/>In an effort to push forward the multi-messenger science achieved in the merger of non-vacuum, compact object mergers, this project seeks the continued development of a distributed and adaptive code infrastructure that models such mergers within relativistic, magnetohydrodynamics. In addition to magnetic effects, realistic equations of state, along with neutrino heating and cooling, will be adopted in simulations of the merger and post-merger of compact object binaries. In addition, adopting a model of a high density phase transition in a piecewise-polytropic equation of state agnostic to the underlying physics, the range of dynamics for such transitions in mergers will be studied.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.