1210.4544 (Qing-Quan Jiang)

A note on black hole spectroscopy in the tunneling mechanism    [PDF]

Qing-Quan Jiang

There is a long-standing belief that a black hole horizon should be endowed with a quantum area spectrum given by $A_n=\gamma l_p^2 n$. In recent work, it has been claimed, in the tunneling mechanism, the area spacing parameter is given by $\gamma=4$. This spacing level is encouraging, since it is not only in full agreement with the Hod's result, but more importantly, is smaller than that given by Bekenstein as well as the one obtained in the context of black hole quasinormal modes. Unfortunately, the Bohr-Sommerfeld quantization rule used in these work is somewhat misleading, so its resulting area spacing seems unconvincing. In this paper, we associate a tunneling process with a large $n$ transition of a quantum black hole to straighten this misunderstanding out. Then, under the new interpretation for a tunneling process, we refine the Hod's idea and Kunstatter's treatment to revisit the black hole spectroscopy in the tunneling mechanism. It is finally found that, in the tunneling mechanism, the area spacing parameter is really fixed by $\gamma=4$. In addition, we follow the new interpretation for a tunneling process to comment on the Bohr-Sommerfeld quantization rule used in previous work.

View original: http://arxiv.org/abs/1210.4544