Generazione di onde gravitazionali post-merging nella coalescenza di sistemi binari di buchi neri

Standing to mathematics, time evolution of slightly perturbed black holes could be described by a superposition of exponentially damped oscillations. Frequencies and damping times shall depend only on the parameters of the back hole, mass and spin angular momentum, as told by the no-hair theorem. In this work oscillation modes are calculated in the case of perturbed Schwarzschild black holes, i.e. in the spherically symmetric case and without angular momentum. Calculations bring to a wave equation with an effecive potential, whoose analitic can be sketched out by setting boundary conditions. Due to these conditions, these modes are called Quasi-Normal Modes (QNMs). An analytic solution is though prohibitive. Other numeric or semi-analytic methods are therefore illustrated, in particular te WKB method is in detail exposed. Finally a solution for the lower order modes is obtained, and the mode's frequencies and damping times depend only on the black hole's mass, and not by the type of perturbation. The analysis is then extended to Kerr black holes with nonnull angular momentum. In this case frequencies depend only on the black hole's mass and angular momentum. By accurately measuring more than one mode, this modes can be compared, and if it turned out that they depend only on two parameters, the no-hair theorem would be verified. Subsequently comparison is done with the results of the GW150914 event, i.e. the gravitational inspiral-merger-ringdown signal emitted by two black holes and detected by the LIGO interferometers in the states one year ago. The merger of this binary sistem generated a perturbed black hole, and the capted ringdown signal is analysed in search of the dominant quasi-normal modes. Unfortunately GW150914 does not give strong evidence of this modes, since on the ringdown was observed for a very short lapse of time. Finally, one could ask himself what would be necessary to gain more evidence of these modes. To have more stringent tests, experiments would need a higher signal noise-ratio, and a more massive binary black hole sysyem to merge.