High overtones of dirac perturbations of a Schwarzschild black hole and the area spectrum of quantum black holes

Abstract

We find high overtones of the Dirac quasi-normal (QN) spectrum of a Schwarzschild black hole (Sbh), by Leaver's method. At high overtones, the spacing of the imaginary part of the QN spectrum is equidistant (Im omegan+1- Im omegan = i/8M , where M is the black hole mass). This can also be analytically obtained by means of a Born approximation. At high overtones, the real part of omegan goes to zero. Finally, we comment this result in the context of Hod's conjecture on highly damped QNMs and the area spectrum of (quantum) black holes.