Every astrophysically realistic simulation needs accurate initial data and in this talk I will present methods to obtain such solutions for a variety of problems. In particular I will focus on a new initial data formulation to solve the full set of Einstein equations for spacetimes that contain a black hole under general conditions. As an application I will present nonaxisymmetric, self-gravitating tori in the presence of a black hole whose spin is tilted with respect to the angular momentum of the disk. The numerical implementation of these methods is done in the context of the Compact Object CALculator (COCAL) code whose purpose is to provide initial data for any general-relativistic system.
In the second part of this talk I will address two questions: First, how one can distinguish a binary black hole undergoing a merger from a binary neutron star if the individual compact companions have masses that fall inside the so-called mass gap of 3-5 solar masses? I will show that although the ringdown phase is indistinguishable from the perturbed Kerr spacetime, the inspiral phase can lead to measurable differences. Second, whether any of the known neutron stars that exhibit ergoregions are dynamically stable? If not, can we identify any dynamically stable ergostar? The answer to these questions will have consequences to the conjecture by Komissarov that a horizon is not necessary for the energy creation of a relativistic jet.