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 ω n+1 − Im ω n = 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 ω n 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.