Abstract By using the entanglement entropy method, this paper calculates the statistical entropy of the Bose and Fermi fields in thin films, and derives the Bekenstein--Hawking entropy and its correction term on the background of a rotating and charged black string. Here, the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string. Taking into account the effect of the generalized uncertainty principle on quantum state density, it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model. These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect. The ultraviolet cut-off in the brick-wall model is not reasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the viewpoint of quantum statistical mechanics, the correction value of Bekenstein--Hawking entropy is obtained. This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.
Received: 20 August 2008
Revised: 06 November 2008
Accepted manuscript online:
PACS:
04.70.Dy
(Quantum aspects of black holes, evaporation, thermodynamics)
Fund: Project supported by the Natural
Science Foundation of Shanxi Province, China (Grant No 2006011012)
and the Doctoral Scientific Research Starting Foundation of Shanxi
Datong University, China.
Cite this article:
Zhao Ren(赵仁), Wu Yue-Qin (武月琴), and Zhang Li-Chun(张丽春) Entropy of a rotating and charged black string to all orders in the Planck length 2009 Chin. Phys. B 18 1749
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