Quasi-normal oscillations of a schwarzschild black hole

The modes of oscillation of a Schwarzschild black hole are determined within an analytic framework. These quasi-normal modes are related to the bound states of the inverted black hole potential which is approximated by the inverted Eckart potential. For a given angular momentum parameter j, the real part of the quasi-normal frequency decreases as the mode number n (or, equivalently, the damping factor) increases, in agreement with the results of numerical studies.