Entropy of the rotating and charged black string to all orders in the Planck length

By using the entanglement entropy method, this paper calculates thestatistical entropy of the Bose and Fermi fields in thin films, andderives the Bekenstein--Hawking entropy and its correction term onthe background of a rotating and charged black string. Here, thequantum field is entangled with quantum states in the blackstring and thin film to the event horizon from outside therotating and charged black string. Taking into account the effect of thegeneralized uncertainty principle on quantum state density, itremoves the difficulty of the divergence of state density nearthe event horizon in the brick-wall model. These calculations anddiscussions imply that high density quantum states near theevent horizon of a black string are strongly correlated with thequantum states in a black string and that black string entropy is aquantum effect. The ultraviolet cut-off in the brick-wall model isnot reasonable. The generalized uncertainty principle should beconsidered in the high energy quantum field near the event horizon.From the viewpoint of quantum statistical mechanics, the correctionvalue of Bekenstein--Hawking entropy is obtained. This allows the fundamental recognitionof the correction value of black string entropy atnonspherical coordinates.