My main scientific interest is currently the two body problem for two black holes. The classical two body problem in physics is formulated for two point-like masses. In Newtonian physics this problem has the well-known solution in terms of Kepler orbits, but do we really understand how two masses move in their mutual gravitational field? As surprising as it may seem at first, the answer to this question is not really known, even if we restrict ourselves to classical, non-quantum physics and to no more than two bodies.
Prof. Dr. Bernd Brügmann