On black hole spectroscopy via quantum tunneling

In recent work [\emph{Quantum tunneling and black hole spectroscopy, Phys. Lett.} B686 (2010) 279, arXiv:0907.4271, by Banerjee et al.], it has been shown, in the tunneling mechanism, the area spacing parameter of a black hole horizon is given by $\gamma=4$. In this paper, by carefully analyzing the tunneling process of the black hole radiation, we interestingly find that the most qualified candidate for a universal area gap in the tunneling mechanism is $\gamma=8\pi$. First, we develop the Banerjee's treatment and the Kunstatter's conjecture to revisit the black hole spectroscopy via quantum tunneling, and find for a real tunneling process, the area spacing parameter is given by the possible value $\gamma\geq 4$. That is, the previous model-dependent area spacing parameters, i.e. $\gamma=8\pi, 4\ln 3, 4$, are all possible in the tunneling mechanism. Finally, some discussions are followed to find, in the tunneling mechanism, $\gamma=8\pi$ is the most qualified candidate for a universal area spacing parameter.