3 Quasi-Normal Modes of Black Holes

One of the most interesting aspects of gravitational wave detection will be the connection with the existence of black holes [201]. Although there are presently several indirect ways of identifying black holes in the universe, gravitational waves emitted by an oscillating black hole will carry a unique fingerprint which would lead to the direct identification of their existence.

As we mentioned earlier, gravitational radiation from black hole oscillations exhibits certain characteristic frequencies which are independent of the processes giving rise to these oscillations. These “quasi-normal” frequencies are directly connected to the parameters of the black hole (mass, charge and angular momentum) and for stellar mass black holes are expected to be inside the bandwidth of the constructed gravitational wave detectors.

The perturbations of a Schwarzschild black hole reduce to a simple wave equation which has been studied extensively. The wave equation for the case of a Reissner–Nordström black hole is more or less similar to the Schwarzschild case, but for Kerr one has to solve a system of coupled wave equations (one for the radial part and one for the angular part). For this reason the Kerr case has been studied less thoroughly. Finally, in the case of Kerr–Newman black holes we face the problem that the perturbations cannot be separated in their angular and radial parts and thus apart from special cases [124] the problem has not been studied at all.