** **The motion of strongly gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations, combining fluid dynamics with general relativity. Centuries after their advent, the solution to these equations remains mathematically and computationally difficult. The difficulties manifest themselves in numerical simulations of cosmological fluid flows, or binary neutron-star inspiral. Our work focuses on formulating and implementing novel, well-posed hydrodynamic schemes, suitable for inspiral simulations and gravitational-wave detector applications, with mathematical and computational applications in academia and industry.

The recent observations of the inspiral and merger of binary black holes by the LIGO-Virgo collaboration, which marked the beginning of the era of gravitational wave astronomy, make this work very timely: additional observations from binary neutron star or black hole-neutron star binary mergers are anticipated over the next years. The NCSA Gravity Group’s research is aimed at mathematically and computationally exploring the theory of neutron stars, in order to improve our understanding of fundamental physical laws and reveal how nature operates on scales where our current understanding breaks down. The expected direct detection of gravitational waves from binary neutron star inspiral and merger has opened up the possibility of using LIGO-Virgo to study the behavior of matter under the extreme conditions of a neutron star interior – the dense matter equation of state in crust and core – which is inaccessible to earth labs or astronomical observations in the electromagnetic spectrum. Improved modeling and understanding of neutron-star gravitational waveforms will aid in LIGO-Virgo search and parameter estimation.