The inspiral and merger of binary neutron stars (BNS) is one of the most promising potential sources of gravitational waves for ground-based detectors like Advanced LIGO. BNS mergers are also likely a source of counterpart electromagnetic radiation. It is important to perform simulations of BNS to better understand and model their gravitational wave emission as well as their electromagnetic emission. The parameter space of BNS binaries is quite large, and one aspect that has not been well studied in neutron star spin.

In this thesis, we focus on investigating spinning neutron stars in compact object binaries. Using the SpEC code, developed by the SXS collaboration, we begin by presenting a new code to create initial data for binary neutron stars with arbitrary spins. We introduce a novel method of measuring neutron star spin, and show that it is accurate and robust. We evolve several spinning binary configurations and show that their properties agree remarkably well with Post-Newtonian predictions. We also show that we are able to control the eccentricity of the binaries to ~ 0.1%.

Thereafter, we proceed to extend our code to black hole.neutron star (BHNS) binaries. We create many data sets across the BHNS parameter space, varying neutron star spin magnitude, spin direction, compactness, and black hole mass, spin and spin direction. We are able to create initial data sets with neutron star spins near the massshedding limit, and nearly extremal black hole spins.

Finally, we investigate spurious gravitational radiation in binary black hole systems. We study its parameter space dependence, by introducing three diagnostics, investigating them as a function of black hole spin and black hole separation, and comparing two different methods of constructing initial data.