Black hole spectroscopy from a class of Plebanski and Demianski space-times

Recently, via adiabatic invariance, Majhi and Vagenas quantized the horizon area of the general class of a static spherically symmetric space-time. Very recently, applying the period of the gravity system with respect to the Euclidean time, Zeng and Liu derived area spectra of a Schwarzschild black hole and a Kerr black hole. It is noteworthy that the preceding methods are not useful for the quasi-normal modes. In this paper, based on those works, and as a further study, adopting near horizon approximation, applying the laws of black hole thermodynamics, we would like to investigate the black hole spectroscopy from a class of Plebanski and Demianski space-times by using two different methods. The result shows that the area spectrum of the black hole is ΔA = 8π∫_P², which confirms the initial proposal of Bekenstein, and the result is consistent with that already obtained by Maggiore with quasi-normal modes. (author)