Quantization of Horizon Area from the NUT-Kerr-Newman Black Hole

The aim of this Letter is to investigate the spectroscopy of the NUT-Kerr-Newman black hole by improving the method of revisited adiabatic invariant quantity. We present the modified expression of the adiabatic invariant quantity in the dragged–Painlevé coordinate system, and derive the spectroscopy of the black hole via revisited adiabatic invariant quantity, using Bohr–Sommerfeld quantization rule and the first law of the black hole thermodynamics. The result shows that the area and entropy spectra are respectively equally spaced and independent of black hole parameters and the area spectrum of the black hole is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta A=8\pi l_{P}^{2}$\end{document}, which confirms the initial proposal of Bekenstein. It is noteworthy that there is no need to impose the small angular momentum limit and small charge limit in contrast to the quasinormal mode method.