Black Holes: Perturbation Theory and Quasinormal Modes in Binary Systems
Black Holes are the most exotic and fascinating astrophysical objects in nature. Recent experimental advances have made the existence of such objects in our universe unquestionable. Although, from a theoretical point of view, they are characterized by only three parameters, mass, charge and angular momentum, what made Subrahmanyan Chandrasekhar characterize them as the "most simple and beautiful consequence of Einstein's relativity theory", the physical processess that take place in the vicinity of such objects presents a high degree of complexity. In particular, the study of scattering of fields in the vicinity of black holes constitutes an important problem currently in study. The curved geometry of spacetime in the proximites of black holes makes the evolution equations of the fields difficult to solve. However, in some idealized situations, it is possible to obtain analytical results, whose validity can be tested comparing them with numerical solutions. In this work we discuss the process of scattering of scalar fields in the vicinity of a black hole binary, in a idealized situation where it is possible to separate the wave equation. The method used to solve the equations is analogous to what has already being done in the case of the scattering around a rotating black hole, described by the Kerr metric. With the analytical results we can determine the quasinormal modes, i.e. the relaxation modes of a black hole after being perturbed by a external field.