One of the most well known predictions of the Theory of General Relativity (GR) is the existence of spacetime oscillations that propagate throughout the universe, the so called, gravitational waves (GWs).  Recent observations of GWs involve binary systems, that is, two astronomical objects that are close enough for their mutual gravitational attraction to cause them to orbit around a common center of mass as they get closer and closer until a catastrophic collision event occurs, releasing huge amounts of energy and angular momentum in the form of gravitational radiation.

The main goal of our work is to investigate how classical and semi-classical effects in GR that are well know to spacetimes containing a single astrophysical object (a star or a black hole), namely the quasinormal ringdown, the Penrose process and Hawking radiation extend to binary systems. To that end, we will work on two fronts: The first is a semi-analytic approach in which we will study exact (and analytic) solutions of Einstein's equations that approximate binary black hole systems in static equilibrium. The second is a numeric approach in which we (with the help of international collaborators) will use numeric approximations of binary systems that are no longer in static equilibrium for our investigations. In this qualification monograph, due to space and time limitations, we shall restrict ourselves to the most mature and well explored results of our work so far: The penrose process and quasinormal modes of a static binary of two extremally charged constituents. In the conclusion we shall list and discuss briefly the remainder of our undergoing research efforts.